On a p-curl system arising in electromagnetism

TL;DR

This paper establishes the existence and asymptotic behavior of solutions to a p-curl system in electromagnetism, exploring the limit as p approaches infinity and analyzing related variational inequalities.

Contribution

It introduces new existence results for p-curl systems with nonlinearities and boundary conditions, and investigates the asymptotic limit leading to curl-constrained variational inequalities.

Findings

Existence of solutions for p-curl systems with power nonlinearity.

Asymptotic analysis as p tends to infinity leading to variational inequalities.

Results on stability, uniqueness, and continuous dependence of solutions.

Abstract

We prove existence of solution of a $p$-curl type evolutionary system arising in electromagnetism with a power nonlinearity of order $p$, $1<p<\infty$, assuming natural tangential boundary conditions. We consider also the asymptotic behaviour in the power obtaining, when $p$ tends to infinity, a variational inequality with a curl constraint. We also discuss the existence, uniqueness and continuous dependence on the data of the solutions to general variational inequalities with curl constraints dependent on time, as well as the asymptotic stabilization in time towards the stationary solution with and without constraint.