Quasi-potentials of the entropy functionals for scalar conservation laws
Giovanni Bellettini, Federica Caselli, Mauro Mariani
TL;DR
This paper studies the quasi-potential problem for entropy cost functionals in scalar conservation laws, showing that quasi-potentials match the integral of an Einstein entropy for non-entropic solutions.
Contribution
It establishes that quasi-potentials for entropy functionals are equivalent to the integral of Einstein entropy, providing a new characterization for non-entropic solutions.
Findings
Quasi-potentials coincide with the integral of Einstein entropy.
The results apply to scalar conservation laws with smooth fluxes.
Provides a new variational characterization of entropy solutions.
Abstract
We investigate the quasi-potential problem for the entropy cost functionals of non-entropic solutions to scalar conservation laws with smooth fluxes. We prove that the quasi-potentials coincide with the integral of a suitable Einstein entropy.
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Taxonomy
TopicsNavier-Stokes equation solutions · Geometric Analysis and Curvature Flows · Cosmology and Gravitation Theories