Exponential decay for fractional Schr\"odinger parabolic problems

TL;DR

This paper investigates the exponential decay behavior of solutions to fractional Schrödinger parabolic equations in various L^p spaces, characterizing potentials that ensure exponential decay of solutions.

Contribution

It provides a comprehensive analysis of exponential decay in L^p spaces for fractional Schrödinger equations and characterizes potentials that guarantee this decay.

Findings

Identifies conditions on potentials for exponential decay

Analyzes the semigroup's exponential type across L^p spaces

Provides a characterization of decay behavior for solutions

Abstract

We discuss exponential decay in $L^p(R^N)$, $1\leq p \leq \infty$, of solutions of a fractional Schr\"odinger parabolic equation with a locally uniformly integrable potential. The exponential type of the semigroup of solutions is considered and its dependence in $1\leq p \leq \infty$ is addressed. We characterise a large class of potentials for which solutions decay exponentially.