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 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.
| 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 |
Keywords
- L2-energy method
- Nonlinear stable
- Planar rarefaction wave
- Viscous conservation law
ASJC Scopus subject areas
- Mathematics(all)