Initial-boundary value problem for a fractional type degenerate heat equation

Abstract

In this paper, we study a fractional type degenerate heat equation posed in bounded domains. We show the existence of solutions for measurable and bounded non-negative initial data, and homogeneous Dirichlet boundary condition. The nonlocal diffusion effect relies on an inverse of the [Formula: see text]-fractional Laplacian operator, and the solvability is proved for any [Formula: see text].