Fractional flows driven by subdifferentials in Hilbert spaces

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3 Citations (Scopus)

Abstract

This paper presents an abstract theory on well-posedness for time-fractional evolution equations governed by subdifferential operators in Hilbert spaces. The proof relies on a regularization argument based on maximal monotonicity of time-fractional differential operators as well as energy estimates based on a nonlocal chain-rule formula for subdifferentials. Moreover, it will be extended to a Lipschitz perturbation problem. These abstract results will be also applied to time-fractional nonlinear PDEs such as time-fractional porous medium, fast diffusion, p-Laplace parabolic, Allen-Cahn equations.

Original languageEnglish
Pages (from-to)809-862
Number of pages54
JournalIsrael Journal of Mathematics
Volume234
Issue number2
DOIs
Publication statusPublished - 2019 Oct 1

ASJC Scopus subject areas

  • Mathematics(all)

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