### 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

### Cite this

**Renormalized dissipative solutions for quasilinear anisotropic degenerate parabolic equations.** / Takagi, Satoru.

Research output: Contribution to journal › Article

*Communications in Applied Analysis*, vol. 9, no. 3-4, pp. 481-503.

}

TY - JOUR

T1 - Renormalized dissipative solutions for quasilinear anisotropic degenerate parabolic equations

AU - Takagi, Satoru

PY - 2005/7/1

Y1 - 2005/7/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=26844552436&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=26844552436&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:26844552436

VL - 9

SP - 481

EP - 503

JO - Communications in Applied Analysis

JF - Communications in Applied Analysis

SN - 1083-2564

IS - 3-4

ER -