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
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M3 - Article
AN - SCOPUS:22844455120
SN - 0002-9947
VL - 352
SP - 1203
EP - 1215
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
IS - 3
ER -