TITLE

Existence and uniqueness of weak solutions for a class of fractional superdiffusion equations

AUTHOR(S)
Qiu, Meilan; Mei, Liquan; Yang, Ganshang
PUB. DATE
January 2017
SOURCE
Advances in Difference Equations;1/2/2017, Vol. 2017 Issue 1, p1
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
In this paper, we consider the existence and uniqueness of weak solutions for a class of fractional superdiffusion equations with initial-boundary conditions. For a multidimensional fractional drift superdiffusion equation, we just consider the simplest case with divergence-free drift velocity $u \in L^{2}(\Omega)$ only depending on the spatial variable x. Finally, exploiting the Schauder fixed point theorem combined with the Arzelà-Ascoli compactness theorem, we obtain the existence and uniqueness of weak solutions in the standard Banach space $C([0,T]; H_{0}^{1}(\Omega))$ for a class of fractional superdiffusion equations.
ACCESSION #
120497560

 

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