Stochastic Effects for the Reaction-Duffing Equation with Wick-Type Product
نویسندگان
چکیده
منابع مشابه
Soliton Solutions for the Wick-Type Stochastic KP Equation
and Applied Analysis 3 S n1 . S n −1 consisting of all formal expansion X ∑ α bαHα with bα ∈ R such that ‖X‖−1,−q ∑ α b 2 α 2N −qα < ∞ for some q ∈ N, by the action 〈X, x〉 α bα, cα α! and bα, cα is the usual inner product in R. X♦Y α,β aα, bβ Hα β is called the Wick product of X and Y , for X ∑ α aαHα, Y ∑ α bαHα ∈ S n−1 with aα, bα ∈ R. We can prove that the spaces S R , S R ∗ S n1 , and S n−1...
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It has been known for a while that a nonlinear equation driven by singular noise must be interpreted in the re-normalized, or Wick, form. For the stochastic Burgers equation, Wick nonlinearity forces the solution to be a generalized process no matter how regular the random perturbation is, whence the curse. On the other hand, certain multiplicative random perturbations of the deterministic Burg...
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In this paper we study mathematically the eigenvalue problem for stochastic elliptic partial differential equation of Wick type. Using the Wick-product and the Wiener-Itô chaos expansion, the stochastic eigenvalue problem is reformulated as a system of an eigenvalue problem for a deterministic partial differential equation and elliptic partial differential equations by using the Fredholm altern...
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ژورنال
عنوان ژورنال: Advances in Mathematical Physics
سال: 2016
ISSN: 1687-9120,1687-9139
DOI: 10.1155/2016/9062343