Well-posedness for the Cauchy problem for a fractional porous medium equation with variable density in one space dimension

TL;DR

This paper investigates the existence and uniqueness of bounded solutions for a one-dimensional fractional nonlinear porous medium equation with variable density, addressing fundamental questions about well-posedness in this mathematical context.

Contribution

It establishes conditions for well-posedness of the fractional porous medium equation with variable density in one dimension, advancing understanding of such nonlinear PDEs.

Findings

Proved existence of bounded solutions under certain conditions.

Established uniqueness of solutions for the problem.

Provided insights into the behavior of solutions in fractional porous media.

Abstract

We study existence and uniqueness of bounded solutions to a fractional nonlinear porous medium equation with a variable density, in one space dimension.