Regularity of weak solutions of the Cauchy problem to a fractional porous medium equation

Shan Li,Lei Zhang

doi:10.1186/s13661-015-0286-8

Abstract

This paper concerns the regularity of the weak solutions of the Cauchy problem to a fractional porous medium equation with a forcing term. In the recent work (Fan et al. in Comput. Math. Appl. 67:145-150, 2014), the authors established the existence of the weak solution and the uniqueness of the weak energy solution. In this paper, we show that the every nonnegative bounded weak energy solution is indeed a strong solution.

Highlights

This is a sequel of the previous work [ ]
A spectral-tau algorithm is based on the Jacobi operational matrix for a numerical solution of time fractional diffusion-wave equations. (See [ ] for details.) On the other side, Zhang and Li Boundary Value Problems (2015) 2015:28 there is much literature on the porous medium equations
Before we state the main results in this paper, we present some definitions as regards the fractional operator and the weak solutions to the problem ( . )

Summary

Introduction

This is a sequel of the previous work [ ]. We continue to investigate the Cauchy problem to a fractional porous medium equation with a forcing term We assume that u (x) is a bounded and integrable function. Systematic and satisfactory results on the weak solutions to the Cauchy problem to the fractional porous medium problem have been obtained, including the existence, uniqueness, comparison principle, and regularity to the suitable weak solutions.

Results

Conclusion