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Volume 31, Issue 3
Cauchy Problem for a Fractional Parabolic Equation with the Advection

Xitao Li, Meng Xu & Shulin Zhou

DOI: 10.4208/jpde.v31.n3.5

J. Part. Diff. Eq., 31 (2018), pp. 252-273.

Published online: 2018-09

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  • 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.

  • Keywords

Fractional parabolic equation Cauchy problem existence regularity

  • AMS Subject Headings

35A09, 35F10, 35C15

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

lixitao@pku.edu.cn (Xitao Li)

mengxu33@njust.edu.cn (Meng Xu)

szhou@math.pku.edu.cn (Shulin Zhou)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-31-252, author = {Li , XitaoXu , Meng and Zhou , Shulin}, title = {Cauchy Problem for a Fractional Parabolic Equation with the Advection}, journal = {Journal of Partial Differential Equations}, year = {2018}, volume = {31}, number = {3}, pages = {252--273}, 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.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v31.n3.5}, url = {http://global-sci.org/intro/article_detail/jpde/12708.html} }
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 -

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.

Xitao Li, Meng Xu & Shulin Zhou. (2019). Cauchy Problem for a Fractional Parabolic Equation with the Advection. Journal of Partial Differential Equations. 31 (3). 252-273. doi:10.4208/jpde.v31.n3.5
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