Conditions at infinity for the inhomogeneous filtration equation

TL;DR

This paper studies the conditions under which solutions to an inhomogeneous filtration equation exist and are unique in the whole space, focusing on their behavior at infinity with specified boundary conditions.

Contribution

It establishes existence and uniqueness criteria for solutions to the inhomogeneous filtration equation with prescribed behavior at infinity.

Findings

Conditions for existence of solutions at infinity.

Criteria for uniqueness of solutions.

Behavior of solutions with inhomogeneous density.

Abstract

We investigate existence and uniqueness of solutions to the filtration equation with an inhomogeneous density in ${\mathbb R}^N$, approaching at infinity a given continuous datum of Dirichlet type.