Nonlocal time porous medium equation with fractional time derivative

被引：0
|
作者：
Jean-Daniel Djida
Juan J. Nieto
Iván Area
机构：
[1] Universidade de Santiago de Compostela,Instituto de Matemáticas, Departamento de Estatística, Análise Matemática e Optimización
[2] African Institute for Mathematical Sciences,Departamento de Matemática Aplicada II, E.E. Aeronáutica e do Espazo
[3] AIMS-Cameroon,undefined
[4] Universidade de Vigo,undefined
来源：
Revista Matemática Complutense | 2019年 / 32卷
关键词：
Nonlinear fractional diffusion; Regularity; Nonlocal diffusion; Fractional Laplacian; Fractional derivatives; Existence of weak solutions; Energy estimates; 35B65; 26A33; 35K55;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We consider nonlinear nonlocal diffusive evolution equations, governed by a Lévy-type nonlocal operator, fractional time derivative and involving porous medium type nonlinearities. Existence and uniqueness of weak solutions are established using approximating solutions and the theory of maximal monotone operators. Using the De Giorgi–Nash–Moser technique, we prove that the solutions are bounded and Hölder continuous for all positive time.
引用
收藏
页码：273 / 304
页数：31
相关论文
共 50 条
  • [41] Fractional diffusion equation with a generalized Riemann-Liouville time fractional derivative
    Sandev, Trifce
    Metzler, Ralf
    Tomovski, Zivorad
    JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2011, 44 (25)
  • [42] On a time fractional diffusion with nonlocal in time conditions
    Nguyen Hoang Tuan
    Nguyen Anh Triet
    Nguyen Hoang Luc
    Nguyen Duc Phuong
    Advances in Difference Equations, 2021
  • [43] A General Fractional Porous Medium Equation
    de Pablo, Arturo
    Quiros, Fernando
    Rodriguez, Ana
    Luis Vazquez, Juan
    COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2012, 65 (09) : 1242 - 1284
  • [44] Large time behavior for the porous medium equation with convection
    Daniele Andreucci
    Anatoli F. Tedeev
    Meccanica, 2017, 52 : 3255 - 3260
  • [45] OPTIMAL REGULARITY IN TIME AND SPACE FOR THE POROUS MEDIUM EQUATION
    Gess, Benjamin
    Sauer, Jonas
    Tadmor, Eitan
    ANALYSIS & PDE, 2020, 13 (08): : 2441 - 2480
  • [46] Large time behavior for the porous medium equation with convection
    Andreucci, Daniele
    Tedeev, Anatoli F.
    MECCANICA, 2017, 52 (13) : 3255 - 3260
  • [47] Life span of solutions to a nonlocal in time nonlinear fractional Schrodinger equation
    Kirane, M.
    Nabti, A.
    ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2015, 66 (04): : 1473 - 1482
  • [48] Implicit difference approximation for the time fractional heat equation with the nonlocal condition
    Karatay, Ibrahim
    Bayramoglu, Serife R.
    Sahin, Ali
    APPLIED NUMERICAL MATHEMATICS, 2011, 61 (12) : 1281 - 1288
  • [49] Inverse Problem for a Time Fractional Parabolic Equation with Nonlocal Boundary Conditions
    Ozbilge, Ebru
    Kanca, Fatma
    Ozbilge, Emre
    MATHEMATICS, 2022, 10 (09)
  • [50] Time-space fractional Schrodinger like equation with a nonlocal term
    Jiang, X. Y.
    EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS, 2011, 193 (01): : 61 - 70
12345