Cauchy Problem for a Fractional Parabolic Equation with the Advection

Xitao Li; Meng Xu; Shulin Zhou

doi:10.4208/jpde.v31.n3.5

Cauchy Problem for a Fractional Parabolic Equation with the Advection

Authors

Xitao Li School of Mathematical Sciences, Peking University, Beijing 100871, China
Meng Xu School of Sciences, Nanjing University of Science and Technology, Nanjing 210094, China
Shulin Zhou School of Mathematical Sciences, Peking University, Beijing 100871, China

DOI:

https://doi.org/10.4208/jpde.v31.n3.5

Keywords:

Fractional parabolic equation;Cauchy problem;existence;regularity

Abstract

In this paper, we give an explicit formula of the solution to Cauchy problem of a fractional parabolic equation with the advection, and then prove the solvability of Cauchy problem and further Schauder-type regularity of the solution under appropriate conditions on the initial value and the right-hand side term.

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Published

2018-09-20

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Issue

Vol. 31 No. 3 (2018)

Section

Articles

How to Cite

Cauchy Problem for a Fractional Parabolic Equation with the Advection. (2018). Journal of Partial Differential Equations, 31(3), 252-273. https://doi.org/10.4208/jpde.v31.n3.5