In this paper, we consider the Cauchy problem for a generic hyperbolic system of conservation laws and assume it is provided by a standard Riemann semigroup of solutions, for summable initial data with small total variation. Then, we introduce an integral functional involving the solutions of the Cauchy problem and investigate when such a functional has a (nontrivial) minimum in case the initial data vary in suitable admissible classes of functions.
Minimization of hyperbolic systems of conservation laws
Rosini, Massimiliano D.
2026-01-01
Abstract
In this paper, we consider the Cauchy problem for a generic hyperbolic system of conservation laws and assume it is provided by a standard Riemann semigroup of solutions, for summable initial data with small total variation. Then, we introduce an integral functional involving the solutions of the Cauchy problem and investigate when such a functional has a (nontrivial) minimum in case the initial data vary in suitable admissible classes of functions.File in questo prodotto:
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