Blow-up sets and Fujita type curves for a degenerate parabolic system with nonlinear boundary conditions

2001 ◽  
Vol 50 (1) ◽  
pp. 629-654 ◽  
Author(s):  
Fernando Quiros ◽  
Julio D. Rossi
Keyword(s):  
Boundary Conditions ◽  
Parabolic System ◽  
Nonlinear Boundary ◽  
Blow Up ◽  
Nonlinear Boundary Conditions ◽  
Degenerate Parabolic System ◽  
Type Curves ◽  
Degenerate Parabolic

On the Critical Fujita Exponent for a Degenerate Parabolic System Coupled Via Nonlinear Boundary Flux

2008 ◽  
Vol 51 (3) ◽  
pp. 785-805 ◽  
Author(s):  
Jun Zhou ◽  
Chunlai Mu
Keyword(s):  
Initial Data ◽  
Boundary Conditions ◽  
Parabolic System ◽  
Nonlinear Boundary ◽  
Blow Up ◽  
Nonlinear Boundary Flux ◽  
Degenerate Parabolic System ◽  
Coupled Boundary Conditions ◽  
Degenerate Parabolic ◽  
Boundary Flux

AbstractIn this paper, we deal with the non-negative solutions of a degenerate parabolic system with nonlinear coupled boundary conditions and non-negative non-trivial compactly supported initial data. The critical Fujita exponents are given and the blow-up rates of the non-global solution are obtained.

scholarly journals GLOBAL EXISTENCE AND BLOW-UP FOR A DOUBLY DEGENERATE PARABOLIC EQUATION SYSTEM WITH NONLINEAR BOUNDARY CONDITIONS

2011 ◽  
Vol 54 (2) ◽  
pp. 309-324
Author(s):  
YONG-SHENG MI ◽  
CHUN-LAI MU ◽  
DENG-MING LIU
Keyword(s):  
Global Existence ◽  
Parabolic System ◽  
Parabolic Equations ◽  
Nonlinear Boundary ◽  
Blow Up ◽  
Nonlinear Boundary Conditions ◽  
Degenerate Parabolic Equations ◽  
Nonlinear Boundary Flux ◽  
Degenerate Parabolic ◽  
Boundary Flux

AbstractIn this paper, we deal with the global existence and blow-up of solutions to a doubly degenerative parabolic system with nonlinear boundary conditions. By constructing various kinds of sub- and super-solutions and using the basic properties of M-matrix, we give the necessary and sufficient conditions for global existence of non-negative solutions, which extend the recent results of Zheng, Song and Jiang (S. N. Zheng, X. F. Song and Z. X. Jiang, Critical Fujita exponents for degenerate parabolic equations coupled via nonlinear boundary flux, J. Math. Anal. Appl. 298 (2004), 308–324), Xiang, Chen and Mu (Z. Y. Xiang, Q. Chen, C. L. Mu, Critical curves for degenerate parabolic equations coupled via nonlinear boundary flux, Appl. Math. Comput. 189 (2007), 549–559) and Zhou and Mu (J. Zhou and C. L Mu, On critical Fujita exponents for degenerate parabolic system coupled via nonlinear boundary flux, Pro. Edinb. Math. Soc. 51 (2008), 785–805) to more general equations.

scholarly journals Existence, blow-up and exponential decay estimates for a system of nonlinear viscoelastic wave equations with nonlinear boundary conditions

2020 ◽  
Vol 19 (1) ◽  
pp. 455-492 ◽  
Author(s):  
Nguyen Thanh Long ◽  
◽  
Hoang Hai Ha ◽  
Le Thi Phuong Ngoc ◽  
Nguyen Anh Triet ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Exponential Decay ◽  
Wave Equations ◽  
Nonlinear Boundary ◽  
Blow Up ◽  
Nonlinear Boundary Conditions ◽  
Decay Estimates ◽  
Nonlinear Viscoelastic ◽  
Viscoelastic Wave
Sign in / Sign up

Export Citation Format

Share Document