Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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BLOW-UP FOR A NON-NEWTON POLYTROPIC FILTRATION SYSTEM WITH NONLINEAR NONLOCAL SOURCE

  • Zhou, Jun (SCHOOL OF MATHEMATICS AND STATISTICS SOUTHWEST UNIVERSITY) ;
  • Mu, Chunlai (COLLEGE OF MATHEMATICS AND PHYSICS CHONGQING UNIVERSITY)
  • Published : 2008.10.31
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Abstract

This paper deals the global existence and blow-up properties of the following non-Newton polytropic filtration system, $${u_t}-{\triangle}_{m,p}u=u^{{\alpha}_1}\;{\int}_{\Omega}\;{\upsilon}^{{\beta}_1}\;(x,\;t)dx,\;{\upsilon}_t-{\triangle}_{n,p}{\upsilon}={\upsilon}^{{\alpha}_2}\;{\int}_{\Omega}\;u^{{\beta}_2}\;(x,{\;}t)dx,$$ 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.

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References

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