scholarly journals DIRECT SOLUTION OF GENERAL ONE-DIMENSIONAL LINEAR PARABOLIC EQUATION VIA AN ABSTRACT PLANCHEREL FORMULA

1969 ◽  
Vol 63 (3) ◽  
pp. 648-654 ◽  
Author(s):  
R. Hersh
Keyword(s):  
Parabolic Equation ◽  
Plancherel Formula ◽  
Linear Parabolic Equation ◽  
Direct Solution ◽  
One Dimensional

Time and space meshes adaptivity for the resolution of a semi-linear heat equation

2021 ◽  
pp. 1-10
Author(s):  
Nejmeddine Chorfi
Keyword(s):  
Parabolic Equation ◽  
Heat Equation ◽  
Order Of Convergence ◽  
Linear Parabolic Equation ◽  
Spectral Elements ◽  
Euler Scheme ◽  
Time Step ◽  
Implicit Euler Scheme ◽  
Linear Heat ◽  
Error Indicators

The aim of this work is to highlight that the adaptivity of the time step when combined with the adaptivity of the spectral mesh is optimal for a semi-linear parabolic equation discretized by an implicit Euler scheme in time and spectral elements method in space. The numerical results confirm the optimality of the order of convergence. The later is similar to the order of the error indicators.

scholarly journals Uniqueness and stability of solutions for a type of parabolic boundary value problem

1989 ◽  
Vol 12 (4) ◽  
pp. 735-739
Author(s):  
Enrique A. Gonzalez-Velasco
Keyword(s):  
Parabolic Equation ◽  
Boundary Value Problem ◽  
Nonnegative Solution ◽  
Boundary Value ◽  
Stability Of Solutions ◽  
General Boundary Conditions ◽  
Boundary Values ◽  
Parabolic Boundary ◽  
One Dimensional ◽  
The One

We consider a boundary value problem consisting of the one-dimensional parabolic equationgut=(hux)x+q, where g, h and q are functions of x, subject to some general boundary conditions. By developing a maximum principle for the boundary value problem, rather than the equation, we prove the uniqueness of a nonnegative solution that depends continuously on boundary values.

scholarly journals On a nonlinear singular one-dimensional parabolic equation and double Laplace decomposition method

2017 ◽  
Vol 9 (1) ◽  
pp. 168781401668653 ◽  
Author(s):  
Hassan Eltayeb Gadain ◽  
Imed Bachar
Keyword(s):  
Parabolic Equation ◽  
Laplace Transform ◽  
Convergence Analysis ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
One Dimensional ◽  
Double Laplace Transform ◽  
Adomian Decomposition ◽  
Laplace Decomposition Method

In this article, the double Laplace transform and Adomian decomposition method are used to solve the nonlinear singular one-dimensional parabolic equation. In addition, we studied the convergence analysis of our problem. Using two examples, our proposed method is illustrated and the obtained results are confirmed.

Controllability Property of a Superlinear Climate System

2013 ◽  
Vol 367 ◽  
pp. 264-269
Author(s):  
Liang Zhang ◽  
Yang Liu
Keyword(s):  
Fixed Point ◽  
Parabolic Equation ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Point Of View ◽  
Climate System ◽  
Linear Parabolic Equation ◽  
Controllability Property

This work concerns a climate system in the point of view of controllability. We obtain by the Kakutani’s fixed point theorem and the controllability property of the linear parabolic equation that the superlinear climate system is null controllable in the case with interior control.

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