Prescribed conditions at infinity for fractional parabolic and elliptic equations with unbounded coefficients

TL;DR

This paper studies the existence, uniqueness, and asymptotic behavior of solutions to fractional parabolic and elliptic equations with unbounded coefficients, under prescribed conditions at infinity, including time-dependent cases.

Contribution

It introduces new conditions at infinity for fractional parabolic and elliptic equations with unbounded coefficients, analyzing solution behavior and asymptotics.

Findings

Established existence and uniqueness of solutions under prescribed conditions at infinity.

Analyzed the asymptotic behavior of solutions for fractional parabolic equations.

Extended results to elliptic equations with similar conditions.

Abstract

We investigate existence and uniqueness of solutions to a class of fractional parabolic equations satisfying prescribed pointwise conditions at infinity (in space), which can be time- dependent. Moreover, we study the asymptotic behaviour of such solutions. We also consider solutions of elliptic equations satisfying appropriate conditions at infinity.