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Fractional flows driven by subdifferentials in Hilbert spaces

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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.

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Authors and Affiliations

  1. Mathematical Institute, Tohoku University, Aoba, Sendai, 980-8578, Japan

    Goro Akagi

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  1. Goro Akagi
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Correspondence to Goro Akagi.

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Dedicated to Professor Mitsuharu Ôtani on the occasion of his 70th birthday

GA is supported by JSPS KAKENHI Grant Number JP18K18715, JP16H03946, JP16K05199, JP17H01095 and by the Alexander von Humboldt Foundation and by the Carl Friedrich von Siemens Foundation.

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Akagi, G. Fractional flows driven by subdifferentials in Hilbert spaces. Isr. J. Math. 234, 809–862 (2019). https://doi.org/10.1007/s11856-019-1936-9

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  • DOI: https://doi.org/10.1007/s11856-019-1936-9

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