Nontrivial solutions for a fractional advection dispersion equation in anomalous diffusion

被引：101
|
作者：
Zhang, Xinguang [1 ,3 ]
Liu, Lishan [2 ,3 ]
Wu, Yonghong [3 ,4 ]
Wiwatanapataphee, B. [3 ]
机构：
[1] Yantai Univ, Sch Math & Informat Sci, Yantai 264005, Shandong, Peoples R China
[2] Qufu Normal Univ, Sch Math Sci, Qufu 273165, Shandong, Peoples R China
[3] Curtin Univ, Dept Math & Stat, Perth, WA 6845, Australia
[4] Zhongnan Univ Econ & Law, Sch Math & Stat, Wuhan 430073, Hubei, Peoples R China
来源：
APPLIED MATHEMATICS LETTERS | 2017年 / 66卷
基金：
中国国家自然科学基金;
关键词：
Fractional advection-dispersion equation; Critical point theorem; Anomalous diffusion; Variational methods; LEVY MOTION; EXISTENCE;
D O I：
10.1016/j.aml.2016.10.015
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider the existence of nontrivial solutions for a class of fractional advection-dispersion equations. A new existence result is established by introducing a suitable fractional derivative Sobolev space and using the critical point theorem. (C) 2016 Elsevier Ltd. All rights reserved.
引用
收藏
页码：1 / 8
页数：8
相关论文
共 50 条
  • [31] Existence of solution for a fractional advection dispersion equation in RN
    Zhang, Quan-Guo
    Sun, Hong-Rui
    Li, Ya-Ning
    APPLIED MATHEMATICAL MODELLING, 2014, 38 (15-16) : 4062 - 4075
  • [32] Existence of solution for a general fractional advection–dispersion equation
    César E. Torres Ledesma
    Analysis and Mathematical Physics, 2019, 9 : 1303 - 1318
  • [33] Numerical solution of fractional advection-dispersion equation
    Deng, ZQ
    Singh, VP
    Bengtsson, L
    JOURNAL OF HYDRAULIC ENGINEERING, 2004, 130 (05) : 422 - 431
  • [34] Approximate solution of the fractional advection-dispersion equation
    Jiang, Wei
    Lin, Yingzhen
    COMPUTER PHYSICS COMMUNICATIONS, 2010, 181 (03) : 557 - 561
  • [35] Variational formulation for the stationary fractional advection dispersion equation
    Ervin, VJ
    Roop, JP
    NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2006, 22 (03) : 558 - 576
  • [36] Eulerian derivation of the fractional advection-dispersion equation
    Schumer, R
    Benson, DA
    Meerschaert, MM
    Wheatcraft, SW
    JOURNAL OF CONTAMINANT HYDROLOGY, 2001, 48 (1-2) : 69 - 88
  • [37] FRACTIONAL MODEL EQUATION FOR ANOMALOUS DIFFUSION
    METZLER, R
    GLOCKLE, WG
    NONNENMACHER, TF
    PHYSICA A, 1994, 211 (01): : 13 - 24
  • [38] Analytical and numerical solutions of time and space fractional advection-diffusion-reaction equation
    Jannelli, Alessandra
    Ruggieri, Marianna
    Speciale, Maria Paola
    COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2019, 70 : 89 - 101
  • [39] Analytical and numerical solutions of time-fractional advection-diffusion-reaction equation
    Maji, Sandip
    Natesan, Srinivasan
    APPLIED NUMERICAL MATHEMATICS, 2023, 185 : 549 - 570
  • [40] Numerical solutions of space-fractional advection-diffusion equation with a source term
    Jannelli, Alessandra
    Ruggieri, Marianna
    Speciale, Maria Paola
    INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM-2018), 2019, 2116
12345