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Global solution to Cauchy problem of fractional drift diffusion system with power-law nonlinearity
  • Caihong Gu,
  • Yanbin Tang
Caihong Gu
Huazhong University of Science and Technology
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Yanbin Tang
Huazhong University of Science and Technology
Author Profile

Abstract

In this paper we consider the global existence, regularizing-decay rate and asymptotic behavior of mild solutions to the Cauchy problem of fractional drift diffusion system with power-law nonlinearity. Using the properties of fractional heat semigroup and the classical estimates of fractional heat kernel, we first prove the global-in-time existence and uniqueness of the mild solutions in the frame of mixed time-space Besov space with multi-linear continuous mappings. Then we show the asymptotic behavior and regularizing-decay rate estimates of the solution to equations with power-law nonlinearity by the method of multi-linear operator and the classical Hardy-Littlewood-Sobolev inequality.

Peer review status:UNDER REVIEW

05 Jun 2021Submitted to Mathematical Methods in the Applied Sciences
05 Jun 2021Assigned to Editor
05 Jun 2021Submission Checks Completed
23 Jun 2021Reviewer(s) Assigned