scholarly journals The Blow-Up Behavior of the Heat Equation with Neumann Boundary Conditions

1994 ◽  
Vol 188 (2) ◽  
pp. 641-650 ◽  
Author(s):  
K. Deng
Keyword(s):  
Boundary Conditions ◽  
Heat Equation ◽  
Blow Up ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions

scholarly journals Blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients under Neumann boundary conditions

2020 ◽  
Vol 18 (1) ◽  
pp. 1552-1564
Author(s):  
Huimin Tian ◽  
Lingling Zhang
Keyword(s):  
Boundary Conditions ◽  
Blow Up ◽  
Sufficient Conditions ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Neumann Boundary Conditions ◽  
Reaction Diffusion Equations ◽  
Time Dependent ◽  
Diffusion Equations ◽  
Nonlocal Reaction

Abstract In this paper, the blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients are investigated under Neumann boundary conditions. By constructing some suitable auxiliary functions and using differential inequality techniques, we show some sufficient conditions to ensure that the solution u ( x , t ) u(x,t) blows up at a finite time under appropriate measure sense. Furthermore, an upper and a lower bound on blow-up time are derived under some appropriate assumptions. At last, two examples are presented to illustrate the application of our main results.

scholarly journals FUJITA CRITICAL CURVE FOR A COUPLED DIFFUSION SYSTEM WITH INHOMOGENEOUS NEUMANN BOUNDARY CONDITIONS∗

2016 ◽  
Vol 21 (2) ◽  
pp. 260-269
Author(s):  
Runmei Du ◽  
Minghao Guo
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Diffusion ◽  
Blow Up ◽  
Neumann Boundary ◽  
Critical Curve ◽  
Neumann Boundary Conditions ◽  
Diffusion Equations ◽  
Nonlinear Diffusion Equations ◽  
Exterior Problems ◽  
Coupled Diffusion

In this paper, we establish the blow-up theorems of Fujita type for a class of exterior problems of nonlinear diffusion equations subject to inhomogeneous Neumann boundary conditions. The critical Fujita exponents are determined and it is shown that the critical curve belongs to the blow-up case under any nontrivial initial data.

Global Existence and Blow-Up in Finite Time of Solutions to One Kind of Reaction-Diffusion Educations with Neumann Boundary Conditions

2014 ◽  
Vol 971-973 ◽  
pp. 1017-1020
Author(s):  
Jun Zhou Shao ◽  
Ji Jun Xu
Keyword(s):  
Global Existence ◽  
Boundary Conditions ◽  
Finite Time ◽  
Blow Up ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Neumann Boundary Conditions ◽  
Reaction Diffusion Equations ◽  
Blowing Up ◽  
Processing Techniques

This paper deals with the properties of one kind of reaction-diffusion equations with Neumann boundary conditions based on the comparison principles. The relations of parameter and the situation of the coupled about equations are used to construct the global existent super-solutions and the blowing-up sub-solutions, and then we obtain the conditions of the global existence and blow-up in finite time solutions with the processing techniques of inequality.

scholarly journals Numerical blow-up for nonlinear diffusion equation with neumann boundary conditions

2020 ◽  
Vol 14 (02) ◽  
pp. 80-88
Author(s):  
Ardjouma Ganon ◽  
Manin Mathurin Taha ◽  
N'guessan Koffi ◽  
Augustin Kidjegbo Toure
Keyword(s):  
Diffusion Equation ◽  
Boundary Conditions ◽  
Nonlinear Diffusion ◽  
Blow Up ◽  
Neumann Boundary ◽  
Nonlinear Diffusion Equation ◽  
Neumann Boundary Conditions

scholarly journals Existence of solutions for quasilinear problem with Neumann boundary conditions

2022 ◽  
Vol 40 ◽  
pp. 1-8
Author(s):  
Samira Lecheheb ◽  
Hakim Lakhal ◽  
Messaoud Maouni
Keyword(s):  
Boundary Conditions ◽  
Heat Equation ◽  
Existence Of Solutions ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Compactness Method ◽  
Quasilinear Systems ◽  
Quasilinear Problem

My abstract is:This paper is devoted to the study of the existence of weak solutionsfor quasilinear systems of a partial dierential equations which are the combinationof the Perona-Malik equation and the Heat equation. The proof of the main resultsare based on the compactness method and the motonocity arguments.

Sign in / Sign up

Export Citation Format

Share Document