Nonlinear Stochastic Partial Differential Equations of hyperbolic type driven by L\'{e}vy-type noises

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DateUnpublished - 2016
Number of pages30
Original languageEnglish

Abstract

We study a class of abstract nonlinear stochastic equations of hyperbolic type driven by jump noises,
which covers both beam equations with nonlocal, nonlinear terms and nonlinear wave equations. We derive an
It\^{o} formula for the local mild solution which plays an important role in the proof of our main results. Under
appropriate conditions, we prove the non-explosion and the asymptotic stability of the mild solution.

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