### Abstract

We introduce a new notion of renormalized dissipative solutions for the Cauchy problem of a quasilinear anisotropic degenerate parabolic equation u_{t} + div F(u) = div (A(u)∇ u) +f with locally Lipschitz-continuous flux F and L^{1} 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 L^{1}-setting and construct a renormalized dissipative solution.

Original language | English |
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Pages (from-to) | 481-503 |

Number of pages | 23 |

Journal | Communications in Applied Analysis |

Volume | 9 |

Issue number | 3-4 |

Publication status | Published - 2005 Jul 1 |

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### ASJC Scopus subject areas

- Analysis
- Numerical Analysis
- Modelling and Simulation
- Applied Mathematics