|
|
| |
| ENTROPY SOLUTIONS FOR FIRST-ORDER QUASILINEAR EQUATIONS RELATED TO A BILATERAL OBSTACLE CONDITION IN A BOUNDED DOMAIN |
| |
Citation： |
L. LEVI,G. VALLET.ENTROPY SOLUTIONS FOR FIRST-ORDER QUASILINEAR EQUATIONS RELATED TO A BILATERAL OBSTACLE CONDITION IN A BOUNDED DOMAIN[J].Chinese Annals of Mathematics B,2001,22(1):93~114 |
| Page view： 0
Net amount： 880 |
Authors： |
L. LEVI; G. VALLET |
|
|
| Abstract： |
This paper is devoted to the existence and the uniqueness of the entropy solution for a general scalar conservation law associated with a forced bilateral obstacle condition in a bounded domain of $R^p, p \geq 1$.
The method of penalization is used with a view to obtaining an existence result. However, the former only gives uniform $L^\infty$-estimates and so leads in fact to look for an Entropy Measure-Valued Solution, according to the specific properties of bounded sequences in $L^\infty$. The uniqueness of this EMVS is proved. Classically, it first ensures the existence of a bounded and measurable function U entropy solution and then the strong convergence in $L^q$ of approximate solutions to U. |
Keywords： |
Obstacle problem, Measure-valued solution, Scalar conservation law |
Classification： |
35L65, 35R35, 35L85 |
|
|
Download PDF Full-Text
|
|
|
|
