Communications in Mathematical Sciences

Volume 14 (2016)

Number 3

A numerical method for the computation of tangent vectors to $2 \times 2$ hyperbolic systems of conservation laws

Pages: 683 – 704

DOI: https://dx.doi.org/10.4310/CMS.2016.v14.n3.a5

Authors

Michael Herty (RWTH, Aachen University, IGPM, Aachen, Germany)

Benedetto Piccoli (Department of Mathematics, Rutgers University, Camden, New Jersey, U.S.A.)

Abstract

We are interested in the development of a numerical method for solving optimal control problems governed by hyperbolic systems of conservation laws. The main difficulty of computing the derivative in the case of shock waves is resolved in the presented scheme. Our approach is based on a combination of a relaxation approach in combination with a numerical scheme to resolve the evolution of the tangent vectors. Numerical results for optimal control problems are presented.

Keywords

conservation laws, optimization, tangent vectors

2010 Mathematics Subject Classification

35L65, 49K20, 49K40

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Published 26 February 2016