### Abstract

This paper is concerned with the asymptotic behavior of the solution toward the planar rarefaction wave r( j) connecting u+ and u- for the scalar viscous conservation law in two space dimensions. We assume that the initial data U_{0}(X,y) tends to constant states u± as x -»±00, respectively. Then, the convergence rate to r(j) of the solution u(t,i,j/) is investigated without the smallness conditions of |_{+} -u_{-}| and the initial disturbance. The proof is given by elementary Z/2-energy method.

Original language | English |
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Pages (from-to) | 1203-1215 |

Number of pages | 13 |

Journal | Transactions of the American Mathematical Society |

Volume | 352 |

Issue number | 3 |

Publication status | Published - 2000 |

### Keywords

- L2-energy method
- Nonlinear stable
- Planar rarefaction wave
- Viscous conservation law

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Nishikawa, M., & Nishihara, K. (2000). Asymptotics toward the planar rarefaction wave for viscous conservation law in two space dimensions.

*Transactions of the American Mathematical Society*,*352*(3), 1203-1215.