Strong dissipativity of generalized time-fractional derivatives and quasi-linear (stochastic) partial differential equations

Liu W, Röckner M, da Silva JL (2021)
Journal of Functional Analysis 281(8): 109135.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Liu, Wei; Röckner, MichaelUniBi; da Silva, Jose Luis
Abstract / Bemerkung
In this paper strong dissipativity of generalized time-fractional derivatives on Gelfand triples of properly in time weighted L-p-path spaces is proved. In particular, as special cases the classical Caputo derivative and other fractional derivatives appearing in applications are included. As a consequence one obtains the existence and uniqueness of solutions to evolution equations on Gelfand triples with generalized time-fractional derivatives. These equations are of type d/dt (k * u)(t) + A(t, u(t)) = f(t), 0 < t < T, with (in general nonlinear) operators A(t, .) satisfying general weak monotonicity conditions. Here kis a non-increasing locally Lebesgue-integrable nonnegative function on [0, infinity) with lim(s ->infinity) k(s) = 0. Analogous results for the case, where f is replaced by a time-fractional additive noise, are obtained as well. Applications include generalized time-fractional quasi-linear (stochastic) partial differential equations. In particular, time-fractional (stochastic) porous medium and fast diffusion equations with ordinary or fractional Laplace operators and the time-fractional (stochastic) p-Laplace equation are covered. (C) 2021 Elsevier Inc. All rights reserved.
Stichworte
Generalized time-fractional derivative; Strong dissipativity; Weak; monotonicity; Generalized porous medium equation
Erscheinungsjahr
2021
Zeitschriftentitel
Journal of Functional Analysis
Band
281
Ausgabe
8
Art.-Nr.
109135
ISSN
0022-1236
eISSN
1096-0783
Page URI
https://pub.uni-bielefeld.de/record/2957066

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Liu W, Röckner M, da Silva JL. Strong dissipativity of generalized time-fractional derivatives and quasi-linear (stochastic) partial differential equations. Journal of Functional Analysis. 2021;281(8): 109135.
Liu, W., Röckner, M., & da Silva, J. L. (2021). Strong dissipativity of generalized time-fractional derivatives and quasi-linear (stochastic) partial differential equations. Journal of Functional Analysis, 281(8), 109135. https://doi.org/10.1016/j.jfa.2021.109135
Liu, W., Röckner, M., and da Silva, J. L. (2021). Strong dissipativity of generalized time-fractional derivatives and quasi-linear (stochastic) partial differential equations. Journal of Functional Analysis 281:109135.
Liu, W., Röckner, M., & da Silva, J.L., 2021. Strong dissipativity of generalized time-fractional derivatives and quasi-linear (stochastic) partial differential equations. Journal of Functional Analysis, 281(8): 109135.
W. Liu, M. Röckner, and J.L. da Silva, “Strong dissipativity of generalized time-fractional derivatives and quasi-linear (stochastic) partial differential equations”, Journal of Functional Analysis, vol. 281, 2021, : 109135.
Liu, W., Röckner, M., da Silva, J.L.: Strong dissipativity of generalized time-fractional derivatives and quasi-linear (stochastic) partial differential equations. Journal of Functional Analysis. 281, : 109135 (2021).
Liu, Wei, Röckner, Michael, and da Silva, Jose Luis. “Strong dissipativity of generalized time-fractional derivatives and quasi-linear (stochastic) partial differential equations”. Journal of Functional Analysis 281.8 (2021): 109135.

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