Qualitative behaviour of solutions of stochastic reaction-diffusion equations
نویسندگان
چکیده
منابع مشابه
Macroscopic reduction for stochastic reaction-diffusion equations
The macroscopic behavior of dissipative stochastic partial differential equations usually can be described by a finite dimensional system. This article proves that a macroscopic reduced model may be constructed for stochastic reaction-diffusion equations with cubic nonlinearity by artificial separating the system into two distinct slow-fast time parts. An averaging method and a deviation estima...
متن کاملNumerical solutions for fractional reaction-diffusion equations
Fractional diffusion equations are useful for applications where a cloud of particles spreads faster than the classical equation predicts. In a fractional diffusion equation, the second derivative in the spatial variable is replaced by a fractional derivative of order less than two. The resulting solutions spread faster than the classical solutions and may exhibit asymmetry, depending on the fr...
متن کاملApproximation of stochastic advection diffusion equations with finite difference scheme
In this paper, a high-order and conditionally stable stochastic difference scheme is proposed for the numerical solution of $rm Ithat{o}$ stochastic advection diffusion equation with one dimensional white noise process. We applied a finite difference approximation of fourth-order for discretizing space spatial derivative of this equation. The main properties of deterministic difference schemes,...
متن کاملLocal Behaviour of Solutions of Stochastic Integral Equations
Let X denote the solution process of the stochastic equation dX{t) = a(X(t)) dt + a(X(t)) d\V{t). In this paper, conditions on a(-) and cr(-) are given under which the sample paths of X are differentiable at t = 0 with probability one. Variations of these results are obtained leading to a new uniqueness criterion for solutions of stochastic equations. If a(-) is Holder continuous with exponent ...
متن کاملExplosive Solutions of Stochastic Reaction-Diffusion Equations in Mean Lp−Norm
The paper is concerned with the problem of non-existence of global solutions for a class of stochastic reaction-diffusion equations of Itô type. Under some sufficient conditions on the initial state, the nonlinear term and the multiplicative noise, it is proven that, in a bounded domain D ⊂ Rd, there exist positive solutions whose mean Lp−norm will blow up in finite time for p ≥ 1, while, if D ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Stochastic Processes and their Applications
سال: 1992
ISSN: 0304-4149
DOI: 10.1016/0304-4149(92)90062-u