Multidimensional Reaction-Diffusion Equations with White Noise Boundary Perturbations
نویسندگان
چکیده
منابع مشابه
Wiener Chaos Versus Stochastic Collocation Methods for Linear Advection-Diffusion-Reaction Equations with Multiplicative White Noise
We compare Wiener chaos and stochastic collocation methods for linear advectionreaction-diffusion equations with multiplicative white noise. Both methods are constructed based on a recursive multistage algorithm for long-time integration. We derive error estimates for both methods and compare their numerical performance. Numerical results confirm that the recursive multistage stochastic colloca...
متن کاملStochastic Partial Differential Equations with Dirichlet White-noise Boundary Conditions
– The paper is devoted to one-dimensional nonlinear stochastic partial differential equations of parabolic type with non homogeneous Dirichlet boundary conditions of white-noise type. We formulate a set of conditions that a random field must satisfy to solve the equation. We show that a unique solution exists and that we can write it in terms of the stochastic kernel related to the problem. Thi...
متن کاملReaction-diffusion equations with nonlinear boundary conditions in narrow domains
Second initial boundary problem in narrow domains of width ǫ ≪ 1 for linear second order differential equations with nonlinear boundary conditions is considered in this paper. Using probabilistic methods we show that the solution of such a problem converges as ǫ ↓ 0 to the solution of a standard reaction-diffusion equation in a domain of reduced dimension. This reduction allows to obtain some r...
متن کاملTime–space White Noise Eliminates Global Solutions in Reaction Diffusion Equations
We prove that perturbing the reaction–diffusion equation ut = uxx + (u+) p (p > 1), with time–space white noise produces that solutions explodes with probability one for every initial datum, opposite to the deterministic model where a positive stationary solution exists.
متن کاملStochastic Equations with Boundary Noise
We study the wellposedness and pathwise regularity of semilinear non-autonomous parabolic evolution equations with boundary and interior noise in an Lp setting. We obtain existence and uniqueness of mild and weak solutions. The boundary noise term is reformulated as a perturbation of a stochastic evolution equation with values in extrapolation spaces.
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: The Annals of Probability
سال: 1994
ISSN: 0091-1798
DOI: 10.1214/aop/1176988495