A kinetic decomposition for singular limits of non-local conservation laws |
| |
Authors: | Frederike Kissling Christian Rohde |
| |
Affiliation: | a Institut für Angewandte Mathematik und Numerische Simulation, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany b Laboratoire Jacques-Louis Lions, Centre National de la Recherche Scientifique, Université Pierre et Marie Curie (Paris 6), 4 Place Jussieu, 75252 Paris, France |
| |
Abstract: | We consider a non-local regularization of nonlinear hyperbolic conservation laws in several space variables. The regularization is motivated by the theory of phase dynamics and is based on a convolution operator. We formulate the initial value problem and begin by deriving a priori estimates which are independent of the regularization parameter. Following Hwang and Tzavaras we establish a kinetic decomposition associated with the problem under consideration, and we conclude that the sequence of solutions generated by the non-local model converges to a weak solution of the corresponding hyperbolic problem. Depending on the scaling introduced in the non-local dispersive term, this weak limit is either a classical Kruzkov solution satisfying all entropy inequalities or, more interestingly, a nonclassical entropy solution in the sense defined by LeFloch, that is, a weak solution satisfying a single entropy inequality and containing undercompressive shock waves possibly selected by a kinetic relation. Finally, we illustrate our analytical conclusions with numerical experiments in one spatial variable. |
| |
Keywords: | Conservation law Entropy solution Nonclassical shock wave Kinetic decomposition Singular limit |
本文献已被 ScienceDirect 等数据库收录! |
|