scholarly journals Critical exponents for a fast diffusive polytropic filtration equation with nonlinear boundary flux

2008 ◽  
Vol 346 (1) ◽  
pp. 55-64 ◽  
Author(s):  
Zhongping Li ◽  
Chunlai Mu
Keyword(s):  
Critical Exponents ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Flux ◽  
Filtration Equation ◽  
Boundary Flux

scholarly journals CRITICAL EXPONENTS FOR A REACTION–DIFFUSION MODEL WITH ABSORPTIONS AND COUPLED BOUNDARY FLUX

2005 ◽  
Vol 48 (1) ◽  
pp. 241-252 ◽  
Author(s):  
Sining Zheng ◽  
Fengjie Li
Keyword(s):  
Diffusion Model ◽  
Critical Exponents ◽  
Nonlinear Boundary ◽  
Blow Up ◽  
Reaction Diffusion ◽  
Nonlinear Boundary Conditions ◽  
Reaction Diffusion Model ◽  
Precise Analysis ◽  
Two Parameters ◽  
Boundary Flux

AbstractThis paper deals with a reaction–diffusion model with inner absorptions and coupled nonlinear boundary conditions of exponential type. The critical exponents are described via a pair of parameters that satisfy a certain matrix equation containing all the six nonlinear exponents of the system. Whether the solutions blow up or not is determined by the signs of the two parameters. A more precise analysis, depending on the geometry of $\varOmega$ and the absorption coefficients, is proposed for the critical sign of the parameters.AMS 2000 Mathematics subject classification: Primary 35K55; 35B33

scholarly journals CRITICAL CURVES FOR A COUPLED SYSTEM OF FAST DIFFUSIVE NEWTONIAN FILTRATION EQUATIONS

2012 ◽  
Vol 86 (3) ◽  
pp. 440-447
Author(s):  
RUNMEI DU ◽  
ZEJIA WANG
Keyword(s):  
Nonlinear Boundary ◽  
Large Time ◽  
Upper And Lower Solutions ◽  
Coupled System ◽  
Dimensional System ◽  
Nonlinear Boundary Flux ◽  
One Dimensional ◽  
Critical Curves ◽  
Nonlinear Anal ◽  
Boundary Flux

AbstractThis paper deals with the large-time behaviour of solutions to the fast diffusive Newtonian filtration equations coupled via the nonlinear boundary sources. A result of Fujita type is obtained by constructing various kinds of upper and lower solutions. In particular, it is shown that the critical global existence curve and the critical Fujita curve concide for the multi-dimensional system. This is quite different from the known results obtained in Wang, Zhou and Lou [‘Critical exponents for porous medium systems coupled via nonlinear boundary flux’, Nonlinear Anal.7(1) (2009), 2134–2140] for the corresponding one-dimensional problem.

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