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Full-Text Articles in Physical Sciences and Mathematics
An Unexpected Limit Of Expected Values, Branko Ćurgus, Robert I. Jewett
An Unexpected Limit Of Expected Values, Branko Ćurgus, Robert I. Jewett
Branko Ćurgus
Let t⩾0. Select numbers randomly from the interval [0,1] until the sum is greater than t . Let α(t) be the expected number of selections. We prove that α(t)=et for 0⩽t⩽1. Moreover, . This limit is a special case of our asymptotic results for solutions of the delay differential equation f′(t)=f(t)-f(t-1) for t>1. We also consider four other solutions of this equation that are related to the above selection process.
Global Well-Posedness And Asymptotic Behavior Of A Class Of Initial-Boundary-Value Problems Of The Kdv Equation On A Finite Domain, Ivonne Rivas, Muhammad Usman, Bingyu Zhang
Global Well-Posedness And Asymptotic Behavior Of A Class Of Initial-Boundary-Value Problems Of The Kdv Equation On A Finite Domain, Ivonne Rivas, Muhammad Usman, Bingyu Zhang
Muhammad Usman
In this paper, we study a class of initial boundary value problem (IBVP) of the Korteweg- de Vries equation posed on a ?nite interval with nonhomogeneous boundary conditions. The IBVP is known to be locally well-posed, but its global L2 a priori estimate is not available and therefore it is not clear whether its solutions exist globally or blow up in finite time. It is shown in this paper that the solutions exist globally as long as their initial value and the associated boundary data are small, and moreover, those solutions decay exponentially if their boundary data decay exponentially.
Renormalization Group Analysis Of Nonlinear Diffusion Equations With Periodic Coefficients, G. A. Braga, Fred Furtado, J. M. Moreira, L. T. Rolla
Renormalization Group Analysis Of Nonlinear Diffusion Equations With Periodic Coefficients, G. A. Braga, Fred Furtado, J. M. Moreira, L. T. Rolla
Fred Furtado
In this paper we present an efficient numerical approach based on the renormalization group method for the computation of self-similar dynamics. The latter arise, for instance, as the long-time asymptotic behavior of solutions to nonlinear parabolic partial differential equations. We illustrate the approach with the veri. cation of a conjecture about the long-time behavior of solutions to a certain class of nonlinear diffusion equations with periodic coefficients. This conjecture is based on a mixed argument involving ideas from homogenization theory and the renormalization group method. Our numerical approach provides a detailed picture of the asymptotics, including the determination of the …
Asymptotic Preconditioning Of Linear Homogeneous Systems Of Differential Equations, William F. Trench
Asymptotic Preconditioning Of Linear Homogeneous Systems Of Differential Equations, William F. Trench
William F. Trench
No abstract provided.
On Nonautonomous Linear Systems Of Differential And Difference Equations With $R$-Symmetric Coefficient Matrices, William F. Trench
On Nonautonomous Linear Systems Of Differential And Difference Equations With $R$-Symmetric Coefficient Matrices, William F. Trench
William F. Trench
No abstract provided.
Asymptotic Behavior Of Linearized Viscoelastic Flow Problem, Yinnian He, Yi Li
Asymptotic Behavior Of Linearized Viscoelastic Flow Problem, Yinnian He, Yi Li
Yi Li
In this article, we provide some asymptotic behaviors of linearized viscoelastic flows in a general two-dimensional domain with certain parameters small and the time variable large.
Asymptotic Behavior Of Solutions Of Asymptotically Constant Coefficient System Of Linear Differential Equations, William F. Trench
Asymptotic Behavior Of Solutions Of Asymptotically Constant Coefficient System Of Linear Differential Equations, William F. Trench
William F. Trench
No abstract provided.
Invertibly Convergent Infinite Products Of Matrices, With Applications To Difference Equations, William F. Trench
Invertibly Convergent Infinite Products Of Matrices, With Applications To Difference Equations, William F. Trench
William F. Trench
No abstract provided.
Asymptotic Behavior Of Solutions Of Poincar'e Difference Equations, William F. Trench
Asymptotic Behavior Of Solutions Of Poincar'e Difference Equations, William F. Trench
William F. Trench
No abstract provided.
Asymptotic Behavior Of Solutions Of A Linear Second Order Difference Equation, William F. Trench
Asymptotic Behavior Of Solutions Of A Linear Second Order Difference Equation, William F. Trench
William F. Trench
No abstract provided.
Efficient Application Of The Schauder-Tychonoff Theorem To Systems Of Functional Differential Equations, William F. Trench
Efficient Application Of The Schauder-Tychonoff Theorem To Systems Of Functional Differential Equations, William F. Trench
William F. Trench
No abstract provided.
Efficient Application Of The Schauder-Tychonoff Theorem To Functional Perturbations Of $X^(N)=0$, William F. Trench
Efficient Application Of The Schauder-Tychonoff Theorem To Functional Perturbations Of $X^(N)=0$, William F. Trench
William F. Trench
No abstract provided.
Global Existence Of Nonoscillatory Solutions Of Perturbed General Disconjugate Equations, William F. Trench, T. Kusano
Global Existence Of Nonoscillatory Solutions Of Perturbed General Disconjugate Equations, William F. Trench, T. Kusano
William F. Trench
No abstract provided.
Linear Perturbations Of A Constant Coefficient Differential Equation Subject To Mild Integral Smallness Conditions, William Trench
Linear Perturbations Of A Constant Coefficient Differential Equation Subject To Mild Integral Smallness Conditions, William Trench
William F. Trench
No abstract provided.
Global Existence Theorems For Solutions Of Nonlinear Differential Equations With Prescribed Asymptotic Behavior, William Trench, T. Kusano
Global Existence Theorems For Solutions Of Nonlinear Differential Equations With Prescribed Asymptotic Behavior, William Trench, T. Kusano
William F. Trench
No abstract provided.
Linear Perturbations Of General Disconjugate Equations, William F. Trench
Linear Perturbations Of General Disconjugate Equations, William F. Trench
William F. Trench
No abstract provided.
Eventual Disconjugacy Of A Linear Differential Equation Ii, William F. Trench
Eventual Disconjugacy Of A Linear Differential Equation Ii, William F. Trench
William F. Trench
No abstract provided.
Asymptotic Behavior Of Solutions Of An N-Th Order Differential Equation, William F. Trench
Asymptotic Behavior Of Solutions Of An N-Th Order Differential Equation, William F. Trench
William F. Trench
No abstract provided.
Asymptotics Of Differential Systems With Deviating Arguments, William F. Trench
Asymptotics Of Differential Systems With Deviating Arguments, William F. Trench
William F. Trench
No abstract provided.
Asymptotic Theory Of Perturbed General Disconjugate Equations, William F. Trench
Asymptotic Theory Of Perturbed General Disconjugate Equations, William F. Trench
William F. Trench
No abstract provided.
Asymptotic Integration Of Linear Differential Equations Subject To Integral Smallness Conditions Involving Ordinary Convergence, William Trench
Asymptotic Integration Of Linear Differential Equations Subject To Integral Smallness Conditions Involving Ordinary Convergence, William Trench
William F. Trench
No abstract provided.
Canonical Forms And Principal Systems For General Disconjugate Equations, William F. Trench
Canonical Forms And Principal Systems For General Disconjugate Equations, William F. Trench
William F. Trench
No abstract provided.