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Well-Posedness of Mild Solutions to Stochastic Parabolic Partial Functional Differential Equations

Well-Posedness of Mild Solutions to Stochastic Parabolic Partial Functional Differential Equations In this paper, we study the well-posedness of mild solutions to stochastic parabolic partial functional differential equations with space–time white noise. Firstly, we establish an existence–uniqueness theorem under the global Lipschitz condition and the linear growth condition. Secondly, we show the existence–uniqueness property under the global/local Lipschitz condition but without assuming the linear growth condition. In particular, we consider the existence and uniqueness under the weaker condition than the Lipschitz condition. Finally, we obtain the nonnegativity and comparison theorems and utilize them to investigate the existence of nonnegative mild solutions under the linear growth condition without assuming the Lipschitz condition. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the Malaysian Mathematical Sciences Society Springer Journals

Well-Posedness of Mild Solutions to Stochastic Parabolic Partial Functional Differential Equations

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia
Subject
Mathematics; Mathematics, general; Applications of Mathematics
ISSN
0126-6705
eISSN
2180-4206
DOI
10.1007/s40840-018-0639-4
Publisher site
See Article on Publisher Site

Abstract

In this paper, we study the well-posedness of mild solutions to stochastic parabolic partial functional differential equations with space–time white noise. Firstly, we establish an existence–uniqueness theorem under the global Lipschitz condition and the linear growth condition. Secondly, we show the existence–uniqueness property under the global/local Lipschitz condition but without assuming the linear growth condition. In particular, we consider the existence and uniqueness under the weaker condition than the Lipschitz condition. Finally, we obtain the nonnegativity and comparison theorems and utilize them to investigate the existence of nonnegative mild solutions under the linear growth condition without assuming the Lipschitz condition.

Journal

Bulletin of the Malaysian Mathematical Sciences SocietySpringer Journals

Published: May 26, 2018

References