Stochastic porous media equation on general measure spaces with increasing Lipschitz nonlinearities

Röckner M, Wu W, Xie Y (2018)
Stochastic Processes and their Applications 128(6): 2131-2151.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
We prove the existence and uniqueness of probabilistically strong solutions to stochastic porous media equations driven by time-dependent multiplicative noise on a general measure space (E, B(E), mu), and the Laplacian replaced by a negative definite self-adjoint operator L. In the case of Lipschitz nonlinearities Psi, we in particular generalize previous results for open E subset of R-d and L=Laplacian to fractional Laplacians. We also generalize known results on general measure spaces, where we succeeded in dropping the transience assumption on L, in extending the set of allowed initial data and in avoiding the restriction to superlinear behavior of Psi at infinity for L-2(mu)-initial data. (C) 2017 Elsevier B.V. All rights reserved.
Stichworte
Wiener process; Porous media equation; Sub-Markovian contractive; semigroup
Erscheinungsjahr
2018
Zeitschriftentitel
Stochastic Processes and their Applications
Band
128
Ausgabe
6
Seite(n)
2131-2151
ISSN
0304-4149
eISSN
1879-209X
Page URI
https://pub.uni-bielefeld.de/record/2920683

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Röckner M, Wu W, Xie Y. Stochastic porous media equation on general measure spaces with increasing Lipschitz nonlinearities. Stochastic Processes and their Applications. 2018;128(6):2131-2151.
Röckner, M., Wu, W., & Xie, Y. (2018). Stochastic porous media equation on general measure spaces with increasing Lipschitz nonlinearities. Stochastic Processes and their Applications, 128(6), 2131-2151. doi:10.1016/j.spa.2017.09.001
Röckner, M., Wu, W., and Xie, Y. (2018). Stochastic porous media equation on general measure spaces with increasing Lipschitz nonlinearities. Stochastic Processes and their Applications 128, 2131-2151.
Röckner, M., Wu, W., & Xie, Y., 2018. Stochastic porous media equation on general measure spaces with increasing Lipschitz nonlinearities. Stochastic Processes and their Applications, 128(6), p 2131-2151.
M. Röckner, W. Wu, and Y. Xie, “Stochastic porous media equation on general measure spaces with increasing Lipschitz nonlinearities”, Stochastic Processes and their Applications, vol. 128, 2018, pp. 2131-2151.
Röckner, M., Wu, W., Xie, Y.: Stochastic porous media equation on general measure spaces with increasing Lipschitz nonlinearities. Stochastic Processes and their Applications. 128, 2131-2151 (2018).
Röckner, Michael, Wu, Weina, and Xie, Yingchao. “Stochastic porous media equation on general measure spaces with increasing Lipschitz nonlinearities”. Stochastic Processes and their Applications 128.6 (2018): 2131-2151.

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