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

Meilan Qiu; Liquan Mei; Ganshang Yang

doi:10.1186/s13662-016-1057-2

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

Meilan Qiu
, Liquan Mei
, Ganshang Yang

School of Mathematics and Statistics

Xi'an Jiaotong University
Yunnan Minzu University
Yunnan Normal University

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

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∈ L²(Ω) 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];H01(Ω)) for a class of fractional superdiffusion equations.

Original language	English
Article number	1
Journal	Advances in Difference Equations
Volume	2017
Issue number	1
DOIs	https://doi.org/10.1186/s13662-016-1057-2
State	Published - 1 Dec 2017

Keywords

Arzelà-Ascoli compactness theorem
Schauder’s fixed point theorem
fractional (linear or nonlinear) superdiffusion equation
fractional drift superdiffusion equation

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10.1186/s13662-016-1057-2

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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∈ L2(Ω) only depending on the spatial variable x. Finally, exploiting the Schauder fixed point theorem combined with the Arzel{\`a}-Ascoli compactness theorem, we obtain the existence and uniqueness of weak solutions in the standard Banach space C([0,T];H01(Ω)) for a class of fractional superdiffusion equations.",

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T1 - Existence and uniqueness of weak solutions for a class of fractional superdiffusion equations

AU - Qiu, Meilan

AU - Mei, Liquan

AU - Yang, Ganshang

PY - 2017/12/1

Y1 - 2017/12/1

N2 - 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∈ L2(Ω) 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];H01(Ω)) for a class of fractional superdiffusion equations.

AB - 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∈ L2(Ω) 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];H01(Ω)) for a class of fractional superdiffusion equations.

KW - Arzelà-Ascoli compactness theorem

KW - Schauder’s fixed point theorem

KW - fractional (linear or nonlinear) superdiffusion equation

KW - fractional drift superdiffusion equation

UR - https://www.scopus.com/pages/publications/85007565925

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DO - 10.1186/s13662-016-1057-2

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AN - SCOPUS:85007565925

SN - 1687-1839

VL - 2017

JO - Advances in Difference Equations

JF - Advances in Difference Equations

IS - 1

M1 - 1

ER -

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

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Keywords

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