scholarly journals Remarks on blow-up behavior for a nonlinear diffusion equation with Neumann boundary conditions

1999 ◽  
Vol 127 (1) ◽  
pp. 167-172 ◽  
Author(s):  
Keng Deng ◽  
Mingxi Xu
Keyword(s):  
Diffusion Equation ◽  
Boundary Conditions ◽  
Nonlinear Diffusion ◽  
Blow Up ◽  
Neumann Boundary ◽  
Nonlinear Diffusion Equation ◽  
Neumann Boundary Conditions

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.

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.

Sign in / Sign up

Export Citation Format

Share Document