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Revista Matemática Complutense

, Volume 32, Issue 2, pp 273–304 | Cite as

Nonlocal time porous medium equation with fractional time derivative

  • Jean-Daniel Djida
  • Juan J. Nieto
  • Iván AreaEmail author
Article

Abstract

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.

Keywords

Nonlinear fractional diffusion Regularity Nonlocal diffusion Fractional Laplacian Fractional derivatives Existence of weak solutions Energy estimates 

Mathematics Subject Classification

35B65 26A33 35K55 

Notes

Acknowledgements

The authors are grateful to the reviewers for their helpful comments and remarks that improved a preliminary version of the manuscript.

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Copyright information

© Universidad Complutense de Madrid 2018

Authors and Affiliations

  1. 1.Instituto de Matemáticas, Departamento de Estatística, Análise Matemática e OptimizaciónUniversidade de Santiago de CompostelaSantiago de CompostelaSpain
  2. 2.African Institute for Mathematical Sciences, AIMS-CameroonLimbeCameroon
  3. 3.Departamento de Matemática Aplicada II, E.E. Aeronáutica e do EspazoUniversidade de VigoOurenseSpain

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