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 Rp, p>= 1. The me...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 Rp, p>= 1. The method of penalization is used with a view to obtaining an existence result. However, the former only gives uniform L -estimates and so leads in fact to look for an Entropy Measure-Valued Solution, according to the specific properties of bounded sequences in L . 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 Lq of approximate solutions to U.展开更多
The author presents a simple approach to both regularity and singularity theorems for free boundaries in classical obstacle problems.This approach is based on the monotonicity of several variational integrals,the Fede...The author presents a simple approach to both regularity and singularity theorems for free boundaries in classical obstacle problems.This approach is based on the monotonicity of several variational integrals,the Federer-Almgren dimension reduction and stratification theorems,and some simple PDE arguments.展开更多
This paper presents new results for strong solutions and their coincidence sets of the obstacle problem for linear hyperbolic operators of first order. An inequality similar to the LewyStampacchia ones for elliptic an...This paper presents new results for strong solutions and their coincidence sets of the obstacle problem for linear hyperbolic operators of first order. An inequality similar to the LewyStampacchia ones for elliptic and parabolic problems is shown. Under nondegeneracy conditions the stability of the coincidence set is shown with respect to the variation of the data and with respect to approximation by semilinear hyperbolic problems. These results are applied to the asymptotic stability of the evolution problem with respect to the stationary coercive problem with obstacle.展开更多
文摘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 Rp, p>= 1. The method of penalization is used with a view to obtaining an existence result. However, the former only gives uniform L -estimates and so leads in fact to look for an Entropy Measure-Valued Solution, according to the specific properties of bounded sequences in L . 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 Lq of approximate solutions to U.
基金Project supported by the National Science Foundation (No.DMS 0700517)
文摘The author presents a simple approach to both regularity and singularity theorems for free boundaries in classical obstacle problems.This approach is based on the monotonicity of several variational integrals,the Federer-Almgren dimension reduction and stratification theorems,and some simple PDE arguments.
基金Partially supported by the Project FCT-POCTI/34471/MAT/2000
文摘This paper presents new results for strong solutions and their coincidence sets of the obstacle problem for linear hyperbolic operators of first order. An inequality similar to the LewyStampacchia ones for elliptic and parabolic problems is shown. Under nondegeneracy conditions the stability of the coincidence set is shown with respect to the variation of the data and with respect to approximation by semilinear hyperbolic problems. These results are applied to the asymptotic stability of the evolution problem with respect to the stationary coercive problem with obstacle.
