Renormalized dissipative solutions for quasilinear anisotropic degenerate parabolic equations

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We introduce a new notion of renormalized dissipative solutions for the Cauchy problem of a quasilinear anisotropic degenerate parabolic equation ut + div F(u) = div (A(u)∇ u) +f with locally Lipschitz-continuous flux F and L1 data, and prove the equivalence of such solutions and renormalized entropy solutions in the sense of Bendahmane and Karlsen. As applications, we apply our result to certain relaxation systems in general L1-setting and construct a renormalized dissipative solution.

Original languageEnglish
Pages (from-to)481-503
Number of pages23
JournalCommunications in Applied Analysis
Issue number3-4
Publication statusPublished - 2005 Jul 1


ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Modelling and Simulation
  • Applied Mathematics

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