Stochastic Viscoelastic Wave Equations with Nonlinear Damping and Source Terms
نویسندگان
چکیده
منابع مشابه
On Nonlinear Wave Equations with Degenerate Damping and Source Terms
In this article we focus on the global well-posedness of the differential equation utt − ∆u+ |u|k∂j(ut) = |u|p−1u in Ω× (0, T ), where ∂j is a sub-differential of a continuous convex function j. Under some conditions on j and the parameters in the equations, we obtain several results on the existence of global solutions, uniqueness, nonexistence and propagation of regularity. Under nominal assu...
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We consider an initial-boundary value problem for a nonlinear wave equation in one space dimension. The nonlinearity features the damping term |u|m−1 ut and a source term of the form |u|p−1 u, with m, p > 1. We show that whenever m ≥ p, then local weak solutions are global. On the other hand, we prove that whenever p > m and the initial energy is negative, then local weak solutions cannot be gl...
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*Correspondence: [email protected] School of Mathematical Sciences, Ocean University of China, Qingdao, P.R. China Abstract This work is concerned with the Dirichlet initial boundary problem for a semilinear viscoelastic wave system with nonlinear weak damping and source terms. For nonincreasing positive functions g and h, we show the finite time blow-up of some solutions whose initial data hav...
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Here a; b¿0 and p¿1, m¿1. In case of IBVP, in a bounded domain ⊂Rn with Dirichlet boundary conditions, the following results are known: 1. When a=0, it is proved (see [1, 3, 8, 14, 16]) that the solution blows up in nite time for su ciently large initial data. 2. When b=0; Haraux and Zuazua [5] and Kopackova [7] prove the global existence result for large initial data. The behavior of the solut...
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ژورنال
عنوان ژورنال: Journal of Applied Mathematics
سال: 2014
ISSN: 1110-757X,1687-0042
DOI: 10.1155/2014/450289