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Title: Stochastic nonlinear wave equation with memory driven by compensated Poisson random measures

In this paper, we study a class of stochastic nonlinear wave equation with memory driven by Lévy noise. We first show the existence and uniqueness of global mild solutions using a suitable energy function. Second, under some additional assumptions we prove the exponential stability of the solutions.
Authors:
 [1] ;  [2] ;  [3]
  1. Department of Mathematics, Northwest University, Xi An 710069 (China)
  2. (China)
  3. Jiangsu Provincial Key Laboratory for NSLSCS, School of Mathematical Science, Nanjing Normal University, Nanjing 210023 (China)
Publication Date:
OSTI Identifier:
22250899
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 3; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; FUNCTIONS; MATHEMATICAL SOLUTIONS; NOISE; NONLINEAR PROBLEMS; RANDOMNESS; STABILITY; STOCHASTIC PROCESSES; WAVE EQUATIONS