Existence and Uniqueness for a Class of SPDEs Driven by L\'{e}vy Noise in Hilbert Spaces

Existence and Uniqueness for a Class of SPDEs Driven by L\'{e}vy Noise in Hilbert Spaces

The present paper seeks to prove the existence and uniqueness of solutions to stochastic evolution equations in Hilbert spaces driven by both Poisson random measure and Wiener process with non-Lipschitz drift term. The proof is provided by the theory of measure of noncompactness and condensing opera...

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Main Authors: Majid Zamani, S. Mansour Vaezpour, Erfan Salavati
Format: Article
Language:English
Published: University of Maragheh 2021-08-01
Series:Sahand Communications in Mathematical Analysis
Subjects:
poisson random measure
mild solution
measure of noncompactness
condensing operator
Online Access:https://scma.maragheh.ac.ir/article_244940_8c8f8936b05d0b4c9c5d9997e0ab6315.pdf
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spelling doaj-8c6f459900774d78b8a4a918e6e1755d2021-10-10T05:42:42ZengUniversity of MaraghehSahand Communications in Mathematical Analysis2322-58072423-39002021-08-01183516810.22130/scma.2021.520720.884244940Existence and Uniqueness for a Class of SPDEs Driven by L\'{e}vy Noise in Hilbert SpacesMajid Zamani0S. Mansour Vaezpour1Erfan Salavati2Department of Mathematics and Computer Sciences, Amirkabir University of Technology, Tehran, Iran.Department of Mathematics and Computer Sciences, Amirkabir University of Technology, Tehran, Iran.Department of Mathematics and Computer Sciences, Amirkabir University of Technology, Tehran, Iran.The present paper seeks to prove the existence and uniqueness of solutions to stochastic evolution equations in Hilbert spaces driven by both Poisson random measure and Wiener process with non-Lipschitz drift term. The proof is provided by the theory of measure of noncompactness and condensing operators. Moreover, we give some examples to illustrate the application of our main theorem.https://scma.maragheh.ac.ir/article_244940_8c8f8936b05d0b4c9c5d9997e0ab6315.pdfpoisson random measuremild solutionmeasure of noncompactnesscondensing operator
collection DOAJ
language English
format Article
sources DOAJ
author Majid Zamani
S. Mansour Vaezpour
Erfan Salavati
spellingShingle Majid Zamani
S. Mansour Vaezpour
Erfan Salavati
Existence and Uniqueness for a Class of SPDEs Driven by L\'{e}vy Noise in Hilbert Spaces
Sahand Communications in Mathematical Analysis
poisson random measure
mild solution
measure of noncompactness
condensing operator
author_facet Majid Zamani
S. Mansour Vaezpour
Erfan Salavati
author_sort Majid Zamani
title Existence and Uniqueness for a Class of SPDEs Driven by L\'{e}vy Noise in Hilbert Spaces
title_short Existence and Uniqueness for a Class of SPDEs Driven by L\'{e}vy Noise in Hilbert Spaces
title_full Existence and Uniqueness for a Class of SPDEs Driven by L\'{e}vy Noise in Hilbert Spaces
title_fullStr Existence and Uniqueness for a Class of SPDEs Driven by L\'{e}vy Noise in Hilbert Spaces
title_full_unstemmed Existence and Uniqueness for a Class of SPDEs Driven by L\'{e}vy Noise in Hilbert Spaces
title_sort existence and uniqueness for a class of spdes driven by l\'{e}vy noise in hilbert spaces
publisher University of Maragheh
series Sahand Communications in Mathematical Analysis
issn 2322-5807
2423-3900
publishDate 2021-08-01
description The present paper seeks to prove the existence and uniqueness of solutions to stochastic evolution equations in Hilbert spaces driven by both Poisson random measure and Wiener process with non-Lipschitz drift term. The proof is provided by the theory of measure of noncompactness and condensing operators. Moreover, we give some examples to illustrate the application of our main theorem.
topic poisson random measure
mild solution
measure of noncompactness
condensing operator
url https://scma.maragheh.ac.ir/article_244940_8c8f8936b05d0b4c9c5d9997e0ab6315.pdf
work_keys_str_mv AT majidzamani existenceanduniquenessforaclassofspdesdrivenbylevynoiseinhilbertspaces
AT smansourvaezpour existenceanduniquenessforaclassofspdesdrivenbylevynoiseinhilbertspaces
AT erfansalavati existenceanduniquenessforaclassofspdesdrivenbylevynoiseinhilbertspaces
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