Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-22T04:05:59.969Z Has data issue: false hasContentIssue false
  • English
  • Français

On Some Stochastic Perturbations of Semilinear Evolution Equations

Published online by Cambridge University Press:  20 November 2018

Anna Milian
Anna Milian*
Affiliation:
Cracow University of Technology e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We consider semilinear evolution equations with some locally Lipschitz nonlinearities, perturbed by Banach space valued, continuous, and adapted stochastic process. We show that under some assumptions there exists a solution to the equation. Using the result we show that there exists a mild, continuous, global solution to a semilinear Itô equation with locally Lipschitz nonlinearites. An example of the equation is given.

Keywords

60H20evolution equationmild solutionnon-Lipschitz driftIto integral
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 53 , Issue 3 , 01 September 2010 , pp. 526 - 533
Copyright
Copyright © Canadian Mathematical Society 2010

References

[1] Pazy, A., Semigroups of Linear Operators and Applications to Partial Differential Equations. Applied Mathematical Sciences 44, Springer-Verlag, New York, 1983.Google Scholar
[2] Prato, G. Da and Zabczyk, J., Stochastic Equations in Infinite Dimensions. Encyclopedia of Mathematics and its Applications 44. Cambridge University Press, 1992.Google Scholar