Stability of solutions of semilinear evolution equations with integro-differential operators

TL;DR

This paper investigates the stability and convergence of solutions to semilinear evolution equations involving Le9vy and pseudodifferential operators, establishing conditions under which solutions converge as operators' symbols approach a limit.

Contribution

It introduces new convergence results for solutions of semilinear equations with Le9vy and pseudodifferential operators, expanding understanding of their stability.

Findings

Solutions converge when operator symbols converge to a limit

Results apply to a broad class of pseudodifferential operators

Provides conditions for stability of solutions in semilinear equations

Abstract

We consider solutions of the Cauchy problem for semilinear equations with (possibly) different L\'evy operators. We provide various results on their convergence under the assumption that symbols of the involved operators converge to the symbol of some L\'evy operator. Some results are proved for a more general class of pseudodifferential operators.