scholarly journals Exponential decay for quasilinear parabolic equations in any dimension

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Jian-Wen Sun ◽  
Seonghak Kim
Keyword(s):  
Boundary Value Problem ◽  
Parabolic Equations ◽  
Initial Function ◽  
Constitutive Relations ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Decay Rates ◽  
Quasilinear Parabolic Equations ◽  
Initial Boundary Value ◽  
Quasilinear Parabolic

<p style='text-indent:20px;'>We estimate decay rates of solutions to the initial-boundary value problem for a class of quasilinear parabolic equations in any dimension. Such decay rates depend only on the constitutive relations, spatial domain, and range of the initial function.</p>

scholarly journals Iterative solution of quasilinear parabolic equations by parabolic equations with constant coefficients

1982 ◽  
Vol 24 (2) ◽  
pp. 203-222
Author(s):  
John E. Lavery
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Parabolic Equations ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Quasilinear Parabolic Equations ◽  
Constant Coefficients ◽  
Initial Boundary Value ◽  
Quasilinear Parabolic

AbstractA method for solving quasilinear parabolic equations of the typesthat differs radically from previously known methods is proposed. For each initial-boundary-value problem of one of these types that has boundary conditions of the first kind (second kind), a conjugate initial-boundary-value problem of the other type that has boundary conditions of the second kind (first kind) is defined. Based on the relations connecting the solutions of a pair of conjugate problems, a series of parabolic equations with constant coefficients that do not change step to step is constructed. The method proposed consists in calculating the solutions of the equations of this series. It is shown to have linear convergence. Results of a series of numerical experiments in a finite-difference setting show that one particular implementation of the proposed method has a smaller domain of convergence than Newton's method but that it sometimes converges faster within that domain.

scholarly journals Initial boundary value problem for a class of higher-order n-dimensional nonlinear pseudo-parabolic equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Liming Xiao ◽  
Mingkun Li
Keyword(s):  
Weak Solution ◽  
Boundary Value Problem ◽  
Parabolic Equations ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Higher Order ◽  
Evolution Problem ◽  
Positive Energy ◽  
Initial Boundary Value

AbstractIn this paper, we study the initial boundary value problem for a class of higher-order n-dimensional nonlinear pseudo-parabolic equations which do not have positive energy and come from the soil mechanics, the heat conduction, and the nonlinear optics. By the mountain pass theorem we first prove the existence of nonzero weak solution to the static problem, which is the important basis of evolution problem, then based on the method of potential well we prove the existence of global weak solution to the evolution problem.

scholarly journals Smoothness of solutions of parabolic equations in regions with edges

1981 ◽  
Vol 84 ◽  
pp. 159-168 ◽  
Author(s):  
A. Azzam ◽  
E. Kreyszig
Keyword(s):  
Parabolic Equation ◽  
Boundary Value Problem ◽  
Bounded Domain ◽  
Parabolic Equations ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Smoothness Of Solutions ◽  
Initial Boundary Value ◽  
Simply Connected

We consider the mixed initial-boundary value problem for the parabolic equationin a region Ω × (0, T], where x = (x1, x2) and Ω ⊂ R2 is a simply-connected bounded domain having corners.

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