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- W2022152447 abstract "Dynamical behavior of the following nonlinear stochastic damped waveequations$ nu $utt$+u_t=$Δ$u+f(u)+$ε$dot{W}$on an open bounded domain $DsubsetR^n$, $1leq nleq 3$,, isstudied in the sense of distribution for small $nu, $ε$>0$. Here$nu$ is the parameter that describes the singular perturbation.First, by a decomposition of Markov semigroup defined by (1), astationary solution is constructed which describes the asymptoticbehavior of solution from initial value in state space$H_0^1(D)times L^2(D)$. Then a global measure attractor isconstructed for (1). Furthermore under the case that the stochasticforce is proportional to the square root of singular perturbation,that is ε$=sqrt{nu}$, we study the limit of the behavior of allthe stationary solutions of (1) as $nurightarrow 0$. It is shownthat, by studying a continuity property on $nu$ for the measureattractors of (1), any one stationary solution of the limit equation$u_t=$Δ$u+f(u).$ is a limit point of a stationary solution of (1), as$nurightarrow 0$." @default.
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- W2022152447 date "2010-01-01" @default.
- W2022152447 modified "2023-09-28" @default.
- W2022152447 title "Limit behavior of nonlinear stochastic wave equations with singular perturbation" @default.
- W2022152447 doi "https://doi.org/10.3934/dcdsb.2010.13.175" @default.
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