Blow-up phenomena for a nonlocal p-Laplace equation with Neumann boundary conditions

2016 ◽  
Vol 108 (3) ◽  
pp. 313-324 ◽  
Author(s):  
Menglan Liao ◽  
Wenjie Gao
Keyword(s):  
Boundary Conditions ◽  
Laplace Equation ◽  
Blow Up ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions

scholarly journals Blow-Up in a Slow Diffusive -Laplace Equation with the Neumann Boundary Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Chengyuan Qu ◽  
Bo Liang
Keyword(s):  
Initial Data ◽  
Boundary Conditions ◽  
Bounded Domain ◽  
Laplace Equation ◽  
Finite Time ◽  
Blow Up ◽  
Neumann Boundary ◽  
Initial Energy ◽  
Neumann Boundary Conditions ◽  
Natural Energy

We study a slow diffusive -Laplace equation in a bounded domain with the Neumann boundary conditions. A natural energy is associated to the equation. It is shown that the solution blows up in finite time with the nonpositive initial energy, based on an energy technique. Furthermore, under some assumptions of initial data, we prove that the solutions with bounded initial energy also blow up.

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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