Мақола

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

Meilan QiuSchool of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, ChinaLiquan MeiSchool of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, ChinaGan-Shang YangDepartment of Mathematics, Yunnan Nationalities University, Kunming, 650031, China

2017en

ABI

Аннотация

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.

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DOI: 10.1186/s13662-016-1057-2

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