scholarly journals THE BLOWING-UP PHENOMENON FOR A REACTION DIFFUSION EQUATION WITH A LOCALIZED NON LINEAR SOURCE TERM AND DIRICHLET-NEUMANN BOUNDARY CONDITIONS

2020 ◽  
Vol 60 (1) ◽  
pp. 1-37
Author(s):  
Halima Nachid ◽  
◽  
Firmin K. N’Gohisse ◽  
Yoro Gozo ◽  
◽  
...  
Keyword(s):  
Diffusion Equation ◽  
Boundary Conditions ◽  
Source Term ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Neumann Boundary Conditions ◽  
Reaction Diffusion Equation ◽  
Linear Source ◽  
Blowing Up ◽  
Non Linear

Generic hyperbolicity for scalar parabolic equations

1993 ◽  
Vol 123 (6) ◽  
pp. 1031-1040 ◽  
Author(s):  
Antonio L. Pereira
Keyword(s):  
Diffusion Equation ◽  
Boundary Conditions ◽  
Parabolic Equations ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Neumann Boundary Conditions ◽  
Reaction Diffusion Equation ◽  
Image Position

SynopsisFor the reaction diffusion equationwith homogeneous Neumann boundary conditions, we give results on the generic hyperbolicity of equilibria with respect to a for fixed f and with respect to f for fixed a.

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 Blowup Analysis for a Nonlocal Diffusion Equation with Reaction and Absorption

2012 ◽  
Vol 2012 ◽  
pp. 1-17
Author(s):  
Yulan Wang ◽  
Zhaoyin Xiang ◽  
Jinsong Hu
Keyword(s):  
Diffusion Equation ◽  
Existence Of Solutions ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Nonlocal Diffusion ◽  
Reaction Diffusion Equation ◽  
Optimal Conditions ◽  
All Solutions ◽  
Blowing Up ◽  
Nonlocal Reaction

We investigate a nonlocal reaction diffusion equation with absorption under Neumann boundary. We obtain optimal conditions on the exponents of the reaction and absorption terms for the existence of solutions blowing up in finite time, or for the global existence and boundedness of all solutions. For the blowup solutions, we also study the blowup rate estimates and the localization of blowup set. Moreover, we show some numerical experiments which illustrate our results.

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.

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