On uniqueness of solutions to the surface electromigration equation

TL;DR

This paper studies the uniqueness of solutions to the surface electromigration equation, extending classical plasma physics models with non-local terms, and shows that solutions with certain decay properties are unique.

Contribution

It establishes a uniqueness result for solutions to the SEM equation under decay conditions, generalizing previous results for related plasma physics equations.

Findings

Solutions with strong spatial decay at two times are identical throughout the interval

The SEM equation's solutions are unique under specified decay conditions

Extension of classical uniqueness results to non-local perturbations

Abstract

In this paper we investigate on uniqueness properties of solutions to the surface electromigration (SEM) equation, which is a generalisation of the more classical Zakharov-Kuznetsov equation of plasma physics with non-local perturbation terms. We will show that if the difference of two solutions has a sufficiently strong spatial decay at two different instants of time, then the two solutions coincide on the whole interval of time.