ENTROPY SOLUTIONS FOR DIFFUSION-CONVECTION EQUATIONS WITH PARTIAL DIFFUSIVITY

被引：53

作者：

ESCOBEDO, M

VAZQUEZ, JL

ZUAZUA, E

机构：

[1] UNIV AUTONOMA MADRID, DEPT MATEMAT, E-28049 MADRID, SPAIN

[2] UNIV COMPLUTENSE MADRID, DEPT MATEMATICA APLICADA, E-28040 MADRID, SPAIN

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 1994年 / 343卷 / 02期

关键词：

CONVECTION-DIFFUSION EQUATIONS; SCALAR CONSERVATIONS LAWS; PARTIAL DIFFUSIVITY; ENTROPY CRITERION; UNIQUENESS; VANISHING VISCOSITY;

D O I：

10.2307/2154744

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the Cauchy problem for the following scalar conservation law with partial viscosity u(t) = DELTA(x)u + partial derivative(y)(f(u)), (x, y) is-an-element-of R(N), t>0. The existence of solutions is proved by the vanishing viscosity method. By introducing a suitable entropy condition we prove uniqueness of solutions. This entropy condition is inspired by the entropy criterion introduced by Kruzhkov for hyperbolic conservation laws but it takes into account the effect of diffusion.

引用

页码：829 / 842

页数：14