Second-order Neutral Stochastic Evolution Equations with Heredity
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چکیده
in a real separable Hilbert space H , where the linear (possibly multivalued) operator A : D(A) ⊂H →H is the infinitesimal generator of a strongly continuous cosine family on H , W is a K-valued Wiener process with incremental covariance given by the nuclear operator Q defined on a complete probability space (Ω, ,P) equipped with a normal filtration ( t)t≥0, φ ∈ L(Ω;Cr), and σ is an 0-measurable H-valued random variable independent of W . We develop existence and approximation results by imposing various Lipschitz and Carathéodory-type conditions on the mappings f : [0,T] ×Cr → H (i= 1,2) and g : [0,T]×Cr → BL(K ;H), where K is another real separable Hilbert space and BL(K ;H) is the space of bounded linear operators from K into H . Stochastic partial differential equations (SPDEs) with finite delay arise naturally in the mathematical modeling of various phenomena in the natural and social sciences [19, 20, 22]. As such, researchers have devoted considerable attention to such equations. Just as in the first-order case, where many SPDEs can be described by a single abstract evolution equation and investigated in a unified setting using various methods (e.g., semigroup methods, approximation schemes, and compactness methods), the same is true for the
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تاریخ انتشار 2004