TY - JOUR
T1 - Fractional flows driven by subdifferentials in Hilbert spaces
AU - Akagi, Goro
N1 - Funding Information:
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. publisher-imprint-name Hebrew University Magnes Press article-contains-esm No article-numbering-style Unnumbered article-registration-date-year 2019 article-registration-date-month 10 article-registration-date-day 5 article-toc-levels 0 journal-product ArchiveJournal numbering-style Unnumbered article-grants-type Regular metadata-grant OpenAccess abstract-grant OpenAccess bodypdf-grant Restricted bodyhtml-grant Restricted bibliography-grant Restricted esm-grant OpenAccess online-first true pdf-file-reference BodyRef/PDF/11856_2019_Article_1936.pdf target-type OnlinePDF article-type OriginalPaper journal-subject-primary Mathematics journal-subject-secondary Mathematics, general journal-subject-secondary Algebra journal-subject-secondary Group Theory and Generalizations journal-subject-secondary Analysis journal-subject-secondary Applications of Mathematics journal-subject-secondary Theoretical, Mathematical and Computational Physics journal-subject-collection Mathematics and Statistics open-access false 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.
Publisher Copyright:
© 2019, The Hebrew University of Jerusalem.
PY - 2019/10/1
Y1 - 2019/10/1
N2 - 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.
AB - 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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U2 - 10.1007/s11856-019-1936-9
DO - 10.1007/s11856-019-1936-9
M3 - Article
AN - SCOPUS:85074612411
VL - 234
SP - 809
EP - 862
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
SN - 0021-2172
IS - 2
ER -