scholarly journals Fujita Exponent for a Nonlinear Degenerate Parabolic Equation with Localized Source

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Yulan Wang ◽  
Xiaojun Song ◽  
Chao Ye
Keyword(s):  
Nonlinear Diffusion ◽  
Degenerate Parabolic Equation ◽  
Blow Up ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Localized Source ◽  
Laplacian Equation ◽  
Degenerate Parabolic ◽  
Localized Reaction ◽  
Nonlinear Degenerate

This paper is devoted to understand the blow-up properties of reaction-diffusion equations which combine a localized reaction term with nonlinear diffusion. In particular, we study the critical exponent of ap-Laplacian equation with a localized reaction. We obtain the Fujita exponentqcof the equation.

scholarly journals PULLBACK ATTRACTORS FOR A NON-AUTONOMOUS SEMI-LINEAR DEGENERATE PARABOLIC EQUATION

2010 ◽  
Vol 52 (3) ◽  
pp. 537-554 ◽  
Author(s):  
CUNG THE ANH ◽  
TANG QUOC BAO
Keyword(s):  
Parabolic Equation ◽  
Degenerate Parabolic Equation ◽  
A Priori ◽  
Reaction Diffusion ◽  
A Priori Estimate ◽  
Reaction Diffusion Equations ◽  
Pullback Attractors ◽  
Estimate Method ◽  
Degenerate Parabolic ◽  
Linear Degenerate

AbstractIn this paper, using the asymptotic a priori estimate method, we prove the existence of pullback attractors for a non-autonomous semi-linear degenerate parabolic equation in an arbitrary domain, without restriction on the growth order of the polynomial type non-linearity and with a suitable exponential growth of the external force. The obtained results improve some recent ones for the non-autonomous reaction–diffusion equations.

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.

Complete blow-up for quasilinear degenerate parabolic equations

2000 ◽  
Vol 130 (4) ◽  
pp. 877-908 ◽  
Author(s):  
R. Suzuki
Keyword(s):  
Boundary Condition ◽  
Parabolic Equation ◽  
Parabolic Equations ◽  
Degenerate Parabolic Equation ◽  
Dirichlet Boundary ◽  
Blow Up ◽  
Sufficient Conditions ◽  
Degenerate Parabolic Equations ◽  
Degenerate Parabolic ◽  
Image Position

Non-negative post-blow-up solutions of the quasilinear degenerate parabolic equation in RN (or a bounded domain with Dirichlet boundary condition) are studied. Various sufficient conditions for complete blow-up of solutions are given.

Sign in / Sign up

Export Citation Format

Share Document