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Nonlinear Dissipative Wave Equations With Space-Time Dependent Potentials, Maisa Khader
Nonlinear Dissipative Wave Equations With Space-Time Dependent Potentials, Maisa Khader
Doctoral Dissertations
We study the long time behavior of solutions of the wave equations with absorption abs (u(t, x))[superscript p]⁻¹u(t, x) and variable damping a(t, x)u[subscript t](t, x), where p belongs to (1, n + 2/n - 2) and a(t, x) ~ a₀(1 + abs(x))⁻[superscript alpha](1 + t)⁻[superscript beta] for large abs x and t, a₀ > 0, for alpha belongs to (-infinity, 1), beta belongs to (-1, 1). We established decay estimates for the energy, L² and L[superscript p]⁺¹ norm of the solutions. 1. For alpha belongs to [0, 1), beta belongs to (-1, 1) and alpha + beta belongs to (0, …
Numerical Methods For Fully Nonlinear Second Order Partial Differential Equations, Michael Joseph Neilan
Numerical Methods For Fully Nonlinear Second Order Partial Differential Equations, Michael Joseph Neilan
Doctoral Dissertations
This dissertation concerns the numerical approximations of solutions of fully nonlinear second order partial differential equations (PDEs). The numerical methods and analysis are based on a new concept of weak solutions called moment solutions, which unlike viscosity solutions, are defined by a constructive method called the vanishing moment method. The main idea of the vanishing moment method is to approximate fully nonlinear second order PDEs by a family of fourth order quasi-linear PDEs. Because the method is constructive, we can develop a wealth of convergent numerical discretization methods to approximate fully nonlinear second order PDEs. We first study the numerical …
Covering Maps In The Uniform Category, Brendon L. Labuz
Covering Maps In The Uniform Category, Brendon L. Labuz
Doctoral Dissertations
First, generalized uniform covering maps are classified in terms of subgroups of the uniform fundamental group. Hausdorff, locally uniform joinable, and chain connected covering spaces of a uniformly locally joinable chain connected space are classifieded in terms of closed subgroups of its uniform fundamental group. If the space is also semilocally simply uniform joinable, uniform covering spaces are classified in terms of all subgroups of its uniform fundamental group. Next it is shown that the inverse limit of a strong Mittag-Leer inverse system of Hausdorff uniform covering spaces is a generalized uniform covering space. The question of the converse is …