Existence of stationary solutions for some integro-differential equations with the double scale anomalous diffusion

TL;DR

This paper investigates the existence of stationary solutions for a class of integro-differential equations modeling double scale anomalous diffusion, using fixed point methods and solvability conditions in unbounded domains.

Contribution

It establishes the existence of solutions for integro-differential equations with double scale anomalous diffusion involving fractional Laplacians, extending solvability results to non-Fredholm elliptic operators.

Findings

Proved existence of stationary solutions under certain conditions.

Applied fixed point techniques to integro-differential equations.

Extended solvability analysis to unbounded domains with non-Fredholm operators.

Abstract

The paper is devoted to the investigation of the solvability of an integro-differential equation in the case of the double scale anomalous diffusion with a sum of two negative Laplacians in different fractional powers in R^3. The proof of the existence of solutions relies on a fixed point technique. Solvability conditions for the elliptic operators without the Fredholm property in unbounded domains are used.