The Properties of Solutions on a Class of Parabolic System

2013 ◽  
Vol 753-755 ◽  
pp. 2945-2948
Author(s):  
Zong Hu Xiu
Keyword(s):  
Global Existence ◽  
Parabolic System ◽  
Parabolic Equations ◽  
Blow Up ◽  
Sufficient Conditions ◽  
Initial Value ◽  
Nonlocal Source

By the method of up-sub solutions, we consider a class of parabolic equations with nonlocal source. In the paper, we discuss the relation of the coefficients and the importance of the initial value. We get the sufficient conditions for the global existence and finite blow-up of the solutions.

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.

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.

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