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

Michael Röckner, Weina Wu and Yingchao Xie

Stochastic Processes and their Applications, 2018, vol. 128, issue 6, 2131-2151

Abstract: 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),μ), and the Laplacian replaced by a negative definite self-adjoint operator L. In the case of Lipschitz nonlinearities Ψ, we in particular generalize previous results for open E⊂Rd 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 Ψ at infinity for L2(μ)-initial data.

Keywords: Wiener process; Porous media equation; Sub-Markovian contractive semigroup (search for similar items in EconPapers)
Date: 2018
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S030441491730220X
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:128:y:2018:i:6:p:2131-2151

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.spa.2017.09.001

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().