Investigates minimizing an integral functional related to hyperbolic conservation laws in specific function classes, indicating new insights into solution behavior.
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.
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Buffa et al. (2026) studied this question.
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