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A nonlinear degenerate diffusion equation not in divergence form

  • S. Wang
  • M. Wang
  • Ch.-h. Xie
Article

Abstract.

We consider positive solution of the nonlinear degenerate diffusion equation \(u_t=u^p(\Delta u+u)\) with Dirichlet boundary condition and \(p>1\). It is proved that all positive solutions exist globally if and only if \(\lambda_1\ge 1\), where \(\lambda _1\) is the first eigenvalue of \(-\Delta\) on \(\Omega\) with homogeneous Dirichlet boundary condition.

Key words.Degenerate diffusion equation, global solution, blow up, upper and lower solutions method. 

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Copyright information

© Birkhäuser Verlag, Basel, 2000

Authors and Affiliations

  • S. Wang
    • 1
  • M. Wang
    • 2
  • Ch.-h. Xie
    • 3
  1. 1.Institute of Mathematics, Academia Sinica, Beijing 100080, China, and Department of Mathematics, Henan University, Kaifeng 475001, ChinaChina
  2. 2.Department of Applied Mathematics, Southeast University, Nanjing 210018, ChinaChina
  3. 3.Department of Mathematics, Nanjing University, Nanjing 210093, ChinaChina

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