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

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• 作者：Meilan Qiu ; Liquan Mei ; Ganshang Yang
• 关键词：fractional (linear or nonlinear) superdiffusion equation ; fractional drift superdiffusion equation ; Schauder’s fixed point theorem ; Arzelà ; Ascoli compactness theorem
• 刊名：Advances in Difference Equations
• 出版年：2017
• 出版时间：December 2017
• 年：2017
• 卷：2017
• 期：1
• 全文大小：1636KB
• 刊物主题：Difference and Functional Equations; Mathematics, general; Analysis; Functional Analysis; Ordinary Differential Equations; Partial Differential Equations;
• 出版者：Springer International Publishing
• ISSN：1687-1847
• 卷排序：2017

文摘

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.