Sparse control for VCHE with abstract J

TL;DR

This paper studies a distributed optimal control problem for viscous Camassa-Holm equations, focusing on sparse controls, establishing existence, optimality conditions, and stability analysis related to sparsity parameters.

Contribution

It introduces a framework for sparse control in viscous Camassa-Holm equations, proving existence of solutions and analyzing their stability with respect to sparsity-promoting terms.

Findings

Existence of optimal solutions for sparse control problems.

Derivation of optimality conditions for the control problem.

Analysis of stability of solutions as sparsity parameters vary.

Abstract

We investigate a distributed optimal control problem for the viscous Camassa--Holm equations with sparse controls and a general cost functional. Considering three different forms of sparsity-promoting terms, we prove the existence of optimal solutions, derive the corresponding optimality conditions and analyze the stability of optimal solutions with respect to the sparsity parameter.