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A Kinetic Decomposition for Singular Limits of Non-local Conservation Laws by Frederike Kissling; Philippe G. LeFloch; Christian Rohde is a Mathematics article available to read on EtoBox.

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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.

Who reads A Kinetic Decomposition for Singular Limits of Non-local Conservation Laws?

Author

Frederike Kissling; Philippe G. LeFloch; Christian Rohde

Publisher

Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0022-0396)

Published

2009

Language

EN

Field

Mathematics (Physical Sciences)