THE BLOW-UP PROPERTIES OF SOLUTIONS TO SEMILINEAR HEAT EQUATIONS WITH NEUMANN BOUNDARY CONDITIONS

1998 ◽  
Vol 18 (3) ◽  
pp. 315-325
Author(s):  
Zhigui Lin
Keyword(s):  
Boundary Conditions ◽  
Blow Up ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Heat Equations

scholarly journals Blow-up Rate Estimates and Blow-up Set for a System of Two Heat Equations with Coupled Nonlinear Neumann Boundary Conditions

2020 ◽  
pp. 147-152
Author(s):  
Maan A. Rasheed ◽  
Miroslav Chlebik
Keyword(s):  
Boundary Conditions ◽  
Exponential Type ◽  
Parabolic System ◽  
Blow Up ◽  
Neumann Boundary ◽  
Upper Bounds ◽  
Neumann Boundary Conditions ◽  
Heat Equations ◽  
Blow Up Rate ◽  
Nonlinear Neumann Boundary Conditions

This paper deals with the blow-up properties of positive solutions to a parabolic system of two heat equations, defined on a ball in  associated with coupled Neumann boundary conditions of exponential type. The upper bounds of blow-up rate estimates are derived. Moreover, it is proved that the blow-up in this problem can only occur on the boundary.

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.

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