Chinese Quarterly Journal of Mathematics ›› 2008, Vol. 23 ›› Issue (2): 301-308.

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Existence, Uniqueness and Blow-up of Generalized Solutions to General Nonlinear Filtration Equations 

  

  1. Department of Mathematics,Zhongyuan Institute of Technology
  • Received:2006-04-28 Online:2008-06-30 Published:2023-10-10
  • About author:HUO Zhen-hong(1963-), male, native of Pingyu, Henan, a lecturer of Zhongyuan Institute of Technology, M.S.D., engages in the theories of nonlinear partial differential equations.
  • Supported by:
    Supported by National Science Foundation of China(10572156); Supported by Natural
    Science Foundation of Henan Province(0211010900); Supported by National Science Foundation of Department
    of Education of Henan Province(200510465001)

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Abstract: In this paper, we consider nonnegative solutions to Cauchy problem for the general nonlinear filtration equations ut-Dj(aij(x,t,u)Di+(u))+bi(t,u)Diu+C(x,t,u)=0, and obtain the existence, uniqueness and blow-up in finite time of these solutions under some structure conditions.

Key words: nonlinear filtration equation, Cauchy problem, generalized solution, existence;
uniqueness, blow-up

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