TY - JOUR
T1 - Cauchy Problem for a Fractional Parabolic Equation with the Advection
AU - Li , Xitao
AU - Xu , Meng
AU - Zhou , Shulin
JO - Journal of Partial Differential Equations
VL - 3
SP - 252
EP - 273
PY - 2018
DA - 2018/09
SN - 31
DO - http://doi.org/10.4208/jpde.v31.n3.5
UR - https://global-sci.org/intro/article_detail/jpde/12708.html
KW - Fractional parabolic equation
KW - Cauchy problem
KW - existence
KW - regularity
AB - <p>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.</p>