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February 28, 2026Journal of Hyperbolic Differential Equations0 citations

Minimization of hyperbolic systems of conservation laws

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VBVito BuffaUniversity of FerraraACAndrea CorliUniversity of FerraraDPDiego PallaraUniversity of Salento

Key Points

  • This research aims to explore the minimum of an integral functional linked to hyperbolic conservation laws under summable initial conditions.
  • Examined the Cauchy problem for hyperbolic systems of conservation laws.
  • Assumed standard Riemann semigroup solutions for summable initial data with small total variation.
  • Introduced an integral functional dependent on these solutions and analyzed its properties.
  • Identified conditions under which the integral functional achieves a nontrivial minimum.
  • Demonstrated that varying initial data within admissible function classes influences the minimization outcome.

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.

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Cite This Study

Buffa et al. (2026) studied this question.

synapsesocial.com/papers/69a288170a974eb0d3c04187https://doi.org/10.1142/s0219891626400047
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