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Generalized gradient flows for time-dependent energies and applications to PDEs involving variable exponents
by
Akagi, Goro
, Tanaka, Naoki
in
Analysis
/ Banach spaces
/ Cauchy problems
/ Exponents
/ Gradient flow
/ Hypotheses
/ Mathematics
/ Mathematics and Statistics
/ Nonlinear evolution equations
/ Time dependence
2024
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Generalized gradient flows for time-dependent energies and applications to PDEs involving variable exponents
by
Akagi, Goro
, Tanaka, Naoki
in
Analysis
/ Banach spaces
/ Cauchy problems
/ Exponents
/ Gradient flow
/ Hypotheses
/ Mathematics
/ Mathematics and Statistics
/ Nonlinear evolution equations
/ Time dependence
2024
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Generalized gradient flows for time-dependent energies and applications to PDEs involving variable exponents
by
Akagi, Goro
, Tanaka, Naoki
in
Analysis
/ Banach spaces
/ Cauchy problems
/ Exponents
/ Gradient flow
/ Hypotheses
/ Mathematics
/ Mathematics and Statistics
/ Nonlinear evolution equations
/ Time dependence
2024
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Generalized gradient flows for time-dependent energies and applications to PDEs involving variable exponents
Journal Article
Generalized gradient flows for time-dependent energies and applications to PDEs involving variable exponents
2024
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Overview
The present paper presents an abstract theory for proving (local-in-time) existence of energy solutions to some doubly-nonlinear evolution equations of gradient flow type involving time-dependent subdifferential operators with a quantitative estimate for the local-existence time. Furthermore, the abstract theory is employed to obtain an optimal existence result for some doubly-nonlinear parabolic equations involving space-time variable exponents, which are (possibly) non-monotone in time. More precisely, global-in-time existence of solutions is proved for the parabolic equations.
Publisher
Springer International Publishing,Springer Nature B.V
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