### 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 |
---|---|

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 |

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### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Transactions of the American Mathematical Society*,

*352*(3), 1203-1215.

**Asymptotics toward the planar rarefaction wave for viscous conservation law in two space dimensions.** / Nishikawa, Masataka; Nishihara, Kenji.

Research output: Contribution to journal › Article

*Transactions of the American Mathematical Society*, vol. 352, no. 3, pp. 1203-1215.

}

TY - JOUR

T1 - Asymptotics toward the planar rarefaction wave for viscous conservation law in two space dimensions

AU - Nishikawa, Masataka

AU - Nishihara, Kenji

PY - 2000

Y1 - 2000

N2 - 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 U0(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.

AB - 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 U0(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.

KW - L2-energy method

KW - Nonlinear stable

KW - Planar rarefaction wave

KW - Viscous conservation law

UR - http://www.scopus.com/inward/record.url?scp=22844455120&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=22844455120&partnerID=8YFLogxK

M3 - Article

VL - 352

SP - 1203

EP - 1215

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 3

ER -