Local and blowing-up solutions for an integro-differential diffusion equation and system

TL;DR

This paper investigates initial value problems for a semilinear integro-differential diffusion equation and system, establishing an analogue of Duhamel's principle, local solution existence, and critical exponents akin to Fujita's results.

Contribution

It introduces an analogue of Duhamel's principle for linear integro-differential equations and analyzes local solutions and critical exponents for the nonlinear case.

Findings

Proved the analogue of Duhamel's principle for the linear integro-differential diffusion equation.

Established existence of local mild solutions for the nonlinear equations.

Determined Fujita-type critical exponents for the equations and systems.

Abstract

In the present paper initial problems for the semilinear integro-differential diffusion equation and system are considered. The analogue of Duhamel principle for the linear integro-differential diffusion equation is proved. The results on existence of local mild solutions and Fujita-type critical exponents to the semilinear integro-differential diffusion equation and system are presented.