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2021

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Articles 1171 - 1200 of 1313

Full-Text Articles in Mathematics

Weak And Injective Dimensional Analogues Of Kaplansky's And Auslander's Lemmas For Purity, Laszlo Fuchs, Sang Bum Lee Jan 2021

Weak And Injective Dimensional Analogues Of Kaplansky's And Auslander's Lemmas For Purity, Laszlo Fuchs, Sang Bum Lee

Turkish Journal of Mathematics

We prove a stronger form of an analogue of a Kaplansky lemma on homological dimensions by showing that in a pure-exact sequence $0 \to A \to B \to C \to 0$, the weak dimensions of the modules satisfy $ {\rm w.d.} B = \max\{{\rm w.d.} A, {\rm w.d.} C\}$. We also show that the same equality holds for the injective dimensions whenever the ring is noetherian. In addition, a version of Auslander's lemma for chains of pure submodules $M_{\rho}$ is proved: the weak dimension of the union of the chain equals the supremum of the weak dimensions of the factor …

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On Characterization Of Tripotent Matrices In Triangular Matrix Rings, Tuğba Peti̇k Jan 2021

On Characterization Of Tripotent Matrices In Triangular Matrix Rings, Tuğba Peti̇k

Turkish Journal of Mathematics

Let $\mathfrak{R}$ be a ring with identity $1$ whose tripotents are only $-1$, $0$, and $1$. It is characterized the structure of tripotents in $\mathcal{T}(\mathfrak{R})$ which is the ring of triangular matrices over $\mathfrak{R}$. In addition, when $\mathfrak{R}$ is finite, it is given number of the tripotents in $\mathcal{T}_{n}( \mathfrak{R})$ which is the ring of $n\times n$ dimensional triangular matrices over $\mathfrak{R}$ with $n$ being a positive integer.

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Weak C-Ideals Of A Lie Algebra, Zeki̇ye Çi̇loğlu Şahi̇n, David Anthony Towers Jan 2021

Weak C-Ideals Of A Lie Algebra, Zeki̇ye Çi̇loğlu Şahi̇n, David Anthony Towers

Turkish Journal of Mathematics

A subalgebra $B$ of a Lie algebra $L$ is called a weak c-ideal of $L$ if there is a subideal $C$ of $L$ such that $L=B+C$ and $B\cap C\leq B_{L} $ where $B_{L}$ is the largest ideal of $L$ contained in $B.$ This is analogous to the concept of weakly c-normal subgroups, which has been studied by a number of authors. We obtain some properties of weak c-ideals and use them to give some characterisations of solvable and supersolvable Lie algebras. We also note that one-dimensional weak c-ideals are c-ideals.

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Count Of Genus Zero $J$-Holomorphic Curves In Dimensions Four And Six, Ahmet Beyaz Jan 2021

Count Of Genus Zero $J$-Holomorphic Curves In Dimensions Four And Six, Ahmet Beyaz

Turkish Journal of Mathematics

The abstract should provide clear information about the research and the results obtained, and should not exceed 200 words. The abstract should not contain citations. An application of Gromov--Witten invariants is that they distinguish the deformation types of symplectic structures on a smooth manifold. In this manuscript, it is proven that the use of Gromov--Witten invariants in the class of embedded $J$-holomorphic spheres is restricted. This restriction is in the sense that they cannot distinguish the deformation types of symplectic structures on $X_1\times S^2$ and $X_2\times S^2$ for two minimal, simply connected, symplectic $4$-manifolds $X_1$ and $X_2$ with $b_2^+(X_1)>1$ …

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Bilinear Multipliers Of Small Lebesgue Spaces, Öznur Kulak, Ahmet Turan Gürkanli Jan 2021

Bilinear Multipliers Of Small Lebesgue Spaces, Öznur Kulak, Ahmet Turan Gürkanli

Turkish Journal of Mathematics

Let $G$ be a compact abelian metric group with Haar measure $\lambda $ and $% \hat{G}$ its dual with Haar measure $\mu $. Assume that$~1 < p_{i}

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Some Qualitative Results For Functional Delay Dynamic Equations On Time Scales, Hali̇s Can Koyuncuoğlu Jan 2021

Some Qualitative Results For Functional Delay Dynamic Equations On Time Scales, Hali̇s Can Koyuncuoğlu

Turkish Journal of Mathematics

Let $\mathbb{T}$ be a nonempty, closed, and arbitrary set of real numbers, namely a time scale, and consider the following delay dynamical equation% \[ x^{\Delta}\left( t\right) =a\left( t\right) x\left( t\right) +f\left( t,x\left( \mathbb{\vartheta}\left( t\right) \right) \right) ,\text{ }t\in\mathbb{T}, \] where $\mathbb{\vartheta}$ stands for the abstract delay function. The main goal of this study is three-fold: obtaining the existence of an equi-bounded solution, proving the asymptotic stability of the zero solution, and showing the existence of a periodic solution based on new periodicity concept on time scales for the given delayed equation under certain conditions. In our analysis, we propose an …

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On The Geometry Of Tangent Bundle Of A Hypersurface In $%%Tcimacro{\U{211d} }%%Beginexpansion\Mathbb{R}%Endexpansion^{N+1}$, Semra Yurttançikmaz Jan 2021

On The Geometry Of Tangent Bundle Of A Hypersurface In $%%Tcimacro{\U{211d} }%%Beginexpansion\Mathbb{R}%Endexpansion^{N+1}$, Semra Yurttançikmaz

Turkish Journal of Mathematics

In this paper, tangent bundle $TM$ of the hypersurface $M$ in $% %TCIMACRO{\U{211d} }% %BeginExpansion \mathbb{R} %EndExpansion ^{n+1}$ has been studied. For hypersurface $M$ given by immersion $f:M\rightarrow %TCIMACRO{\U{211d} }% %BeginExpansion \mathbb{R} %EndExpansion ^{n+1},$ considering the fact that $F=df:TM\rightarrow %TCIMACRO{\U{211d} }% %BeginExpansion \mathbb{R} %EndExpansion ^{2n+2}$ is also immersion, $TM$ is treated as a submanifold of $% %TCIMACRO{\U{211d} }% %BeginExpansion \mathbb{R} %EndExpansion ^{2n+2}.$ Firstly, an induced metric which is called rescaled induced metric has been defined on $TM,$ and the Levi-Civita connection has been calculated for this metric. Next, curvature tensors of tangent bundle $TM$ have been obtained. Finally, the orthonormal …

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On The Paper ``A Study On (Strong) Order-Congruences In Ordered Semihypergroups", Niovi Kehayopulu Jan 2021

On The Paper ``A Study On (Strong) Order-Congruences In Ordered Semihypergroups", Niovi Kehayopulu

Turkish Journal of Mathematics

Throughout the paper in the title by Jian Tang, Yanfeng Luo and Xiangyun Xie in Turk J Math 42 (2018) the following lemma has been used. Lemma: Let $(S,*)$ be a semihypergroup and $\rho$ an equivalence relation on S. Then $(i)$ If $\rho$ is a congruence, then $(S/\rho,\otimes)$ is a semihypergroup with respect to the hyperoperation $(a)_\rho\otimes (b)_\rho=\bigcup\limits_{c\in a*b} {(c)_\rho}$. $(ii)$ If $\rho$ is a strong congruence, then $(S/\rho,\otimes)$ is a semigroup with respect to the operation $(a)_\rho\otimes (b)_\rho=(c)_\rho$ for all $c\in a*b$.} The property (i) of the paper is certainly wrong as $\bigcup\limits_{c\in a*b} {(c)_\rho}$ is a subset of …

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Moments And Zero Density Estimates For Dirichlet $L$-Functions, Keiju Sono Jan 2021

Moments And Zero Density Estimates For Dirichlet $L$-Functions, Keiju Sono

Turkish Journal of Mathematics

In this paper, we estimate the density of zeros of primitive Dirichlet $L$-functions in the half-plane $\Re (s)>1/2$, under the assumption of a plausible conjecture on high moments of Dirichlet $L$-functions on the critical line. We conditionally improve the results of Huxley [9], Jutila [13], Heath-Brown [5, 6] and Bourgain [1].

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Optimization Of Mayer Functional In Problems With Discrete And Differential Inclusions And Viability Constraints, Gülseren Çi̇çek, Eli̇mhan N. Mahmudov Jan 2021

Optimization Of Mayer Functional In Problems With Discrete And Differential Inclusions And Viability Constraints, Gülseren Çi̇çek, Eli̇mhan N. Mahmudov

Turkish Journal of Mathematics

This paper derives the optimality conditions for a Mayer problem with discrete and differential inclusions with viable constraints. Applying necessary and sufficient conditions of problems with geometric constraints, we prove optimality conditions for second order discrete inclusions. Using locally adjoint mapping, we derive Euler-Lagrange form conditions and transversality conditions for the optimality of the discrete approximation problem. Passing to the limit, we establish sufficient conditions to the optimal problem with viable constraints. Conditions ensuring the existence of solutions to the viability problems for differential inclusions of second order have been studied in recent years. However, optimization problems of second-order differential …

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Sparse Polynomial Interpolation With Bernstein Polynomials, Erdal İmamoğlu Jan 2021

Sparse Polynomial Interpolation With Bernstein Polynomials, Erdal İmamoğlu

Turkish Journal of Mathematics

We present an algorithm for interpolating an unknown univariate polynomial $f$ that has a $t$ sparse representation ($t

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Reduced Limit Approach To Semilinear Pdes Involving The Fractional Laplacian With Measure Data, Ratan Kumar Giri, Debajyoti Choudhuri Jan 2021

Reduced Limit Approach To Semilinear Pdes Involving The Fractional Laplacian With Measure Data, Ratan Kumar Giri, Debajyoti Choudhuri

Turkish Journal of Mathematics

We study the following partial differential equation (PDE) \begin{align} \begin{split} (-\Delta)^s u + g(x,u) & = \mu\,\,\mbox{in}\,\,\Omega,\\ u & = 0\,\,\mbox{in}\,\,\mathbb{R}^N\setminus\Omega,\label{eqn_abs} \end{split} \end{align} where $(-\Delta)^s$ is the fractional Laplacian operator, $\Omega$ is a bounded domain in $\mathbb{R}^N$ with $\partial\Omega$ being the boundary of $\Omega$, $g(.,.)$ is a nonlinear function defined over $\Omega\times\mathbb{R}$. Let $(\mu_n)_n$ be a sequence of measure in $\Omega$. Assume that there exists a solution $u_n$ with data $\mu_n$, i.e. $u_n$ satisfies the equation (0.1) with $\mu=\mu_n$. We further assume that the sequence of measures weakly converges to $\mu$, while $(u_n)_n$ converges to $u$ in $L^1(\Omega)$. In general, …

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Indecomposable Vector Bundles Via Monads On A Cartesian Product Of Projective Spaces, Damian Maingi Jan 2021

Indecomposable Vector Bundles Via Monads On A Cartesian Product Of Projective Spaces, Damian Maingi

Turkish Journal of Mathematics

The existence of monads on products of projective spaces $P^{a_1}\times\cdots\times\ P^{a_n}$ is nontrivial. In this paper, we construct monads over the polycyclic variety $P^{2n+1}\times\ P^{2n+1}$, we prove that cohomology vector bundle associated to these monads is simple. We also construct a monad on $P^1\times P^1\times\ P^2$. We also study the vector bundles associated to monads and prove stability and simplicity.

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(Co)Limits Of Hom-Lie Crossed Module, Ali̇ Ayteki̇n Jan 2021

(Co)Limits Of Hom-Lie Crossed Module, Ali̇ Ayteki̇n

Turkish Journal of Mathematics

In this paper, we give categorical properties such as pullback, finite product, finite limit, coproduct, colimit and pushout in $\boldsymbol{XHom-Lie/A}$ of the category of Hom-Lie crossed modules.

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Explicit Formulas And Recurrence Relations For Generalized Catalan Numbers, Muhammet Ci̇hat Dağli Jan 2021

Explicit Formulas And Recurrence Relations For Generalized Catalan Numbers, Muhammet Ci̇hat Dağli

Turkish Journal of Mathematics

In this paper, we present an explicit formula and recurrent relation for generalized Catalan numbers, from which we can give corresponding formulas for Schröder numbers, large and small generalized Catalan numbers for the special cases of our results.

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The Kernel Spaces And Fredholmness Of Truncated Toeplitz Operators, Xiaoyuan Yang, Ran Li, Yufeng Lu Jan 2021

The Kernel Spaces And Fredholmness Of Truncated Toeplitz Operators, Xiaoyuan Yang, Ran Li, Yufeng Lu

Turkish Journal of Mathematics

In this paper, we study some conditions about invertible and Fredholm truncated Toeplitz operators which have unique symbols. For $f\in L^\infty$, if $A_f$ is a Fredholm operator, then $f _E\neq 0$ for any $E\subset \mathbb{T}$ with $ E >0$. Moreover \textnormal {ind} $(A_f)=0.$ In particular, if $A_f$ is invertible in $\mathfrak{L}(K_u^2)$, then $f$ is invertible in $L^\infty$. Besides, we give some results about the kernel spaces of truncated Toeplitz operators. For $f \in L^\infty$, we obtain the necessary and sufficient condition that the defect operator $I-A_f^*A_f$ of truncated Toeplitz operator $A_f$ meeting some conditions is compact on the model space …

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A Fourth Order One Step Method For Numerical Solution Of Good Boussinesq Equation, Emre Kirli, Dursun Irk Jan 2021

A Fourth Order One Step Method For Numerical Solution Of Good Boussinesq Equation, Emre Kirli, Dursun Irk

Turkish Journal of Mathematics

In this paper, we investigate the numerical solution of "good" Boussinesq equation by using the quartic B-spline Galerkin method for space discretization and the fourth order one-step method for time discretization.The proposed numerical scheme is analyzed for truncation error. Four test problems are studied. The accuracy and efficiency are measured by computing error norm $L_{\infty }$ and the order of convergence for the proposed method. The results of numerical experiments confirm that the proposed method has a higher accuracy.

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Bounded Invertibility And Separability Of A Parabolic Type Singular Operator In The Space $L_{2}(R^{2})$, Mussakan Muratbekov, Madi Muratbekov, Ainash Suleimbekova Jan 2021

Bounded Invertibility And Separability Of A Parabolic Type Singular Operator In The Space $L_{2}(R^{2})$, Mussakan Muratbekov, Madi Muratbekov, Ainash Suleimbekova

Turkish Journal of Mathematics

In this paper, we consider the operator of parabolic type $$ Lu=\frac{\partial u}{\partial t}-\frac{\partial^{2}u}{\partial x^{2}}+q(x)u, $$ in the space $L_{2}(R^{2})$ with a greatly growing coefficient at infinity. The operator is originally defined on $C_{0}^{\infty}(R^{2})$, where $C_{0}^{\infty}(R^{2})$ is the set of infinitely differentiable and compactly supported functions. \noindent Assume that the coefficient $q(x)$ is a continuous function in $R=(-\infty, \infty)$, and it can be a strongly increasing function at infinity. \noindent The operator $L$ admits closure in space $L_{2}(R^{2})$, and the closure is also denoted by $L$. \noindent In the paper, we proved the bounded invertibility of the operator $L$ in …

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Singular Integral Operators And Maximal Functions With Hardy Space Kernels, Ahmad Al Salman Jan 2021

Singular Integral Operators And Maximal Functions With Hardy Space Kernels, Ahmad Al Salman

Turkish Journal of Mathematics

In this paper, we study singular integrals along compound curves with Hardy space kernels. We introduce a class of bidirectional generalized Hardy Littlewood maximal functions. We prove that the considered singular integrals and the maximal functions are bounded on $L^{p},1

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3-Principalization Over S_3-Fields, Siham Aouissi, Mohamed Talbi, Daniel C. Mayer, Moulay Chrif Ismaili Jan 2021

3-Principalization Over S_3-Fields, Siham Aouissi, Mohamed Talbi, Daniel C. Mayer, Moulay Chrif Ismaili

Turkish Journal of Mathematics

Let $p\equiv 1\,(\mathrm{mod}\,9)$ be a prime number and $\zeta_3$ be a primitive cube root of unity. Then $k=\mathbb{Q}(\sqrt[3]{p},\zeta_3)$ is a pure metacyclic field with group $\mathrm{Gal}(k/\mathbb{Q})\simeq S_3$. In the case that $k$ possesses a $3$-class group $C_{k,3}$ of type $(9,3)$, the capitulation of $3$-ideal classes of $k$ in its unramified cyclic cubic extensions is determined, and conclusions concerning the maximal unramified pro-$3$-extension $k_3^{(\infty)}$, that is the $3$-class field tower of $k$, are drawn.

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Some New Representations Of Hikami's Second-Order Mock Theta Function $\Mathfrak{D}_5(Q)$, Qiuxia Hu Jan 2021

Some New Representations Of Hikami's Second-Order Mock Theta Function $\Mathfrak{D}_5(Q)$, Qiuxia Hu

Turkish Journal of Mathematics

In this paper, a second-order mock theta function $\mathfrak{D}_5(q)$ given by Hikami [11] is studied. By using basic hypergeometric transformation formulae, we attain some new representations of Hikami's mock theta function $\mathfrak{D}_5(q)$. Meanwhile, dual nature of bilateral series associated to mock theta function $\mathfrak{D}_5(q)$ is also discussed.

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On Estimation Of The Number Of Eigenvalues Of The Magnetic Schrödinger Operator In A Three-Dimensional Layer, Araz R. Aliyev, Elshad H. Eyvazov, Shahin Sh. Rajabov Jan 2021

On Estimation Of The Number Of Eigenvalues Of The Magnetic Schrödinger Operator In A Three-Dimensional Layer, Araz R. Aliyev, Elshad H. Eyvazov, Shahin Sh. Rajabov

Turkish Journal of Mathematics

In this paper, we study the magnetic Schrödinger operator in a three-dimensional layer. We obtain an estimate for the number of eigenvalues of this operator lying to the left of the essential spectrum threshold. We show that the magnetic Schrödinger operator to the left of the continuous spectrum threshold can have only a finite number of eigenvalues of infinite multiplicity.

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A Performance Assessment Of An Hdg Method For Second-Order Fredholm Integro-Differential Equation: Existence-Uniqueness And Approximation, Mehmet Fati̇h Karaaslan Jan 2021

A Performance Assessment Of An Hdg Method For Second-Order Fredholm Integro-Differential Equation: Existence-Uniqueness And Approximation, Mehmet Fati̇h Karaaslan

Turkish Journal of Mathematics

In this paper, we obtain the existence--uniqueness of solution to the second-order linear Fredholm integro-differential equation (FIDE) with Dirichlet boundary condition by hybridizable discontinuous Galerkin (HDG) method. A key property of these methods is to eliminate all internal degrees of freedom and to construct a linear system that only includes globally coupled unknowns at the element interfaces. After designing and implementing HDG algorithm, we provide some necessary and sufficient conditions based on the stabilization parameter and kernel function to guarantee the existence-uniqueness of the approximate solution. Then, some numerical examples are carried out to assess the performance of the present …

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An Application Of Semigroup Theory To The Coagulation-Fragmentation Models, Arijit Das, Nilima Das, Jitraj Saha Jan 2021

An Application Of Semigroup Theory To The Coagulation-Fragmentation Models, Arijit Das, Nilima Das, Jitraj Saha

Turkish Journal of Mathematics

We present the existence and uniqueness of strong solutions for the continuous coagulation-fragmentation equation with singular fragmentation and essentially bounded coagulation kernel using semigroup theory of operators. Initially, we reformulate the coupled coagulation-fragmentation problem into the semilinear abstract Cauchy problem (ACP) and consider it as the nonlinear perturbation of the linear fragmentation operator. The existence of the substochastic semigroup is proved for the pure fragmentation equation. Using the substochastic semigroup and some related results for the pure fragmentation equation, we prove the existence of global nonnegative, strong solution for the coagulation-fragmentation equation.

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Secondary Constructions Of (Non)-Weakly Regular Plateaued Functions Over Finite Fields, Si̇hem Mesnager, Ferruh Özbudak, Ahmet Sinak Jan 2021

Secondary Constructions Of (Non)-Weakly Regular Plateaued Functions Over Finite Fields, Si̇hem Mesnager, Ferruh Özbudak, Ahmet Sinak

Turkish Journal of Mathematics

Plateaued (vectorial) functions over finite fields have diverse applications in symmetric cryptography, coding theory, and sequence theory. Constructing these functions is an attractive research topic in the literature. We can distinguish two kinds of constructions of plateaued functions: secondary constructions and primary constructions. The first method uses already known functions to obtain new functions while the latter do not need to use previously constructed functions to obtain new functions. In this work, the first secondary constructions of (non)weakly regular plateaued (vectorial) functions are presented over the finite fields of odd characteristics. We also introduce some recursive constructions of (non)weakly regular …

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Some New Uniqueness And Ulam Stability Results For A Class Of Multi-Terms Fractional Differential Equations In The Framework Of Generalized Caputo Fractional Derivative Using The $\Phi$-Fractional Bielecki-Type Norm, Choukri Derbazi, Zidane Baitiche, Michal Feckan Jan 2021

Some New Uniqueness And Ulam Stability Results For A Class Of Multi-Terms Fractional Differential Equations In The Framework Of Generalized Caputo Fractional Derivative Using The $\Phi$-Fractional Bielecki-Type Norm, Choukri Derbazi, Zidane Baitiche, Michal Feckan

Turkish Journal of Mathematics

In this research article, a novel $\Phi$-fractional Bielecki-type norm introduced by Sousa and Oliveira [23] is used to obtain results on uniqueness and Ulam stability of solutions for a new class of multiterms fractional differential equations in the framework of generalized Caputo fractional derivative. The uniqueness results are obtained by employing Banach' and Perov's fixed point theorems. While the $\Phi$-fractional Gronwall type inequality and the concept of the matrices converging to zero are implemented to examine different types of stabilities in the sense of Ulam-Hyers (UH) of the given problems. Finally, two illustrative examples are provided to demonstrate the validity …

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Computational Identities For Extensions Of Some Families Of Special Numbers And Polynomials, İrem Küçükoğlu, Yilmaz Şi̇mşek Jan 2021

Computational Identities For Extensions Of Some Families Of Special Numbers And Polynomials, İrem Küçükoğlu, Yilmaz Şi̇mşek

Turkish Journal of Mathematics

The main purpose of this paper is to obtain computational identities and formulas for a certain class of combinatorial-type numbers and polynomials. By the aid of the generating function technique, we derive a recurrence relation and an infinite series involving the aforementioned class of combinatorial-type numbers. By applying the Riemann integral to the combinatorial-type polynomials with multivariables, we present some integral formulas for these polynomials, including the Bernoulli numbers of the second kind. By the implementation of the $p$-adic integral approach to the combinatorial-type polynomials with multivariables, we also obtain formulas for the Volkenborn integral and the fermionic $p$-adic integral …

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Zero-Divisor Graphs Of Partial Transformation Semigroups, Kemal Toker Jan 2021

Zero-Divisor Graphs Of Partial Transformation Semigroups, Kemal Toker

Turkish Journal of Mathematics

Let $\mathcal P_{n}$ be the partial transformation semigroup on $X_{n}=\{1,2,\ldots ,n\}$. In this paper, we find the left zero-divisors, right zero-divisors and two sided zero-divisors of $\mathcal P_{n}$, and their numbers. For $n \geq 3$, we define an undirected graph $\Gamma(\mathcal P_{n})$ associated with $\mathcal P_{n}$ whose vertices are the two sided zero-divisors of $\mathcal P_{n}$ excluding the zero element $\theta$ of $\mathcal P_{n}$ with distinct two vertices $\alpha$ and $\beta$ joined by an edge in case $\alpha\beta=\theta =\beta\alpha$. First, we prove that $\Gamma(\mathcal P_{n})$ is a connected graph, and find the diameter, girth, domination number and the degrees of …

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Axes In Non-Associative Algebras, Louis Rowen, Yoav Segev Jan 2021

Axes In Non-Associative Algebras, Louis Rowen, Yoav Segev

Turkish Journal of Mathematics

Fusion rules are laws of multiplication among eigenspaces of an idempotent. This terminology is relatively new and is closely related to axial algebras, introduced recently by Hall, Rehren and Shpectorov. Axial algebras, in turn, are closely related to $3$-transposition groups and Vertex operator algebras. In this paper we consider fusion rules for semisimple idempotents, following Albert in the power-associative case. We examine the notion of an axis in the non-commutative setting and show that the dimension $d$ of any algebra $A$ generated by a pair $a,b$ of (not necessarily Jordan) axes of respective types $(λ,δ)$ and $(λ',δ')$ must be at …

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Global Existence And Blow-Up Of Solutions For Parabolic Equations Involving The Laplacian Under Nonlinear Boundary Conditions., Anass Lamaizi, Abdellah Zerouali, Omar Chakrone, Belhadj Karim Jan 2021

Global Existence And Blow-Up Of Solutions For Parabolic Equations Involving The Laplacian Under Nonlinear Boundary Conditions., Anass Lamaizi, Abdellah Zerouali, Omar Chakrone, Belhadj Karim

Turkish Journal of Mathematics

This paper is concerned with the existence and blow-up of solutions to the following linear parabolic equation: $ ~~ u_t - \Delta u +u = 0 \quad \text{ in } \Omega \times (0,T) $, under nonlinear boundary condition in a bounded domain $ \Omega \subset \mathbb{R}^n $, $n \geq 1$, with smooth boundary. We obtain a threshold result for the global existence of solutions, next we shall prove the existence time $T$ of solution is finite when the initial energy satisfies certain condition.

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