ENTROPY SOLUTIONS FOR DIFFUSION-CONVECTION EQUATIONS WITH PARTIAL DIFFUSIVITY

Authors
ESCOBEDO M VAZQUEZ JL ZUAZUA E
Citation
M. Escobedo et al., ENTROPY SOLUTIONS FOR DIFFUSION-CONVECTION EQUATIONS WITH PARTIAL DIFFUSIVITY, Transactions of the American Mathematical Society, 343(2), 1994, pp. 829-842
Citations number
5
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Transactions of the American Mathematical Society → ACNP
ISSN journal
00029947
Volume
343
Issue
2
Year of publication
1994
Pages
829 - 842
Database
ISI
SICI code
0002-9947(1994)343:2<829:ESFDEW>2.0.ZU;2-Q
Abstract
We consider the Cauchy problem for the following scalar conservation l aw 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 p roved by the vanishing viscosity method. By introducing a suitable ent ropy condition we prove uniqueness of solutions. This entropy conditio n is inspired by the entropy criterion introduced by Kruzhkov for hype rbolic conservation laws but it takes into account the effect of diffu sion.