A variational approach to the inviscous limit of fractional conservation laws
Mauro Mariani, Yannick Sire
TL;DR
This paper studies the limit behavior of control problems for fractional conservation laws as viscosity vanishes, focusing on the convergence of control cost functionals using a variational approach.
Contribution
It introduces a variational framework to analyze the inviscous limit of fractional conservation laws and proves $ ext{Gamma}$-convergence of the control cost functional.
Findings
Established $ ext{Gamma}$-convergence of control cost as viscosity tends to zero
Provided a variational characterization of the inviscid limit
Enhanced understanding of control problems for fractional conservation laws
Abstract
We are concerned with a control problem related to the vanishing \emph{fractional} viscosity approximation to scalar conservation laws. We investigate the -convergence of the control cost functional, as the viscosity coefficient tends to zero.
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Taxonomy
TopicsNavier-Stokes equation solutions · Nonlinear Partial Differential Equations · Stochastic processes and financial applications