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

  • Chaoliang LuoEmail author
  • Shangjiang Guo
  • Aiyu Hou
Article
  • 62 Downloads

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.

Keywords

Stochastic partial functional differential equation Non-Lipschitz Mild solution Existence Uniqueness 

Mathematics Subject Classification

60H15 60G52 34K50 

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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2018

Authors and Affiliations

  1. 1.College of ScienceHunan University of TechnologyZhuzhouPeople’s Republic of China
  2. 2.College of Mathematics and EconometricsHunan UniversityChangshaPeople’s Republic of China

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