BLOW-UP FOR A NON-NEWTON POLYTROPIC FILTRATION SYSTEM WITH NONLINEAR NONLOCAL SOURCE

Title & Authors
BLOW-UP FOR A NON-NEWTON POLYTROPIC FILTRATION SYSTEM WITH NONLINEAR NONLOCAL SOURCE
Zhou, Jun; Mu, Chunlai;

Abstract
This paper deals the global existence and blow-up properties of the following non-Newton polytropic filtration system, $\small{{u_t}-{\triangle}_{m,p}u=u^{{\alpha}_1}\;{\int}_{\Omega}\;{\upsilon}^{{\beta}_1}\;(x,\;t)dx,\;{\upsilon}_t-{\triangle}_{n,p}{\upsilon}={\upsilon}^{{\alpha}_2}\;{\int}_{\Omega}\;u^{{\beta}_2}\;(x,{\;}t)dx,}$ with homogeneous Dirichlet boundary condition. Under appropriate hypotheses, we prove that the solution either exists globally or blows up in finite time depends on the initial data and the relations of the parameters in the system.
Keywords
non-Newtonian polytropic system;nonlocal source;global existence;blow-up;
Language
English
Cited by
1.
LOCAL AND GLOBAL EXISTENCE AND BLOW-UP OF SOLUTIONS TO A POLYTROPIC FILTRATION SYSTEM WITH NONLINEAR MEMORY AND NONLINEAR BOUNDARY CONDITIONS,;;;

대한수학회보, 2013. vol.50. 1, pp.37-56
1.
Blow-up for an evolution p-laplace system with nonlocal sources and inner absorptions, Boundary Value Problems, 2011, 2011, 1, 29
2.
LOCAL AND GLOBAL EXISTENCE AND BLOW-UP OF SOLUTIONS TO A POLYTROPIC FILTRATION SYSTEM WITH NONLINEAR MEMORY AND NONLINEAR BOUNDARY CONDITIONS, Bulletin of the Korean Mathematical Society, 2013, 50, 1, 37
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