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

Zdzislaw Brzezniak

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

Mathematics

Research output: Working paper

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.

Original language	English
Number of pages	30
Publication status	Unpublished - 2016

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ZB+JZ_beamnew_2016_04_27bLicence: Unspecified

Cite this

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

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 anIt\^{o} formula for the local mild solution which plays an important role in the proof of our main results. Underappropriate conditions, we prove the non-explosion and the asymptotic stability of the mild solution.",

author = "Zdzislaw Brzezniak",

year = "2016",

language = "English",

type = "WorkingPaper",

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T1 - Nonlinear Stochastic Partial Differential Equations of hyperbolic type driven by L\'{e}vy-type noises

AU - Brzezniak, Zdzislaw

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N2 - 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 anIt\^{o} formula for the local mild solution which plays an important role in the proof of our main results. Underappropriate conditions, we prove the non-explosion and the asymptotic stability of the mild solution.

AB - 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 anIt\^{o} formula for the local mild solution which plays an important role in the proof of our main results. Underappropriate conditions, we prove the non-explosion and the asymptotic stability of the mild solution.

M3 - Working paper

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

ER -