Random perturbations of reaction-diffusion equations: the quasideterministic approximation
Mark Iosifovich Freidlin · Transactions of the American Mathematical Society · 1988
Random fields ue(t,x) = (u\(t,x),... ,uen(t,x)), defined as the solutions of a system of the PDE due.-^ = Lku% + h(x;u\,...,v?n) + ee.k(t,x) are considered.Here L/t are second-order linear elliptic operators, ç/t are Gaussian white-noise fields, independent for different k, and e is a small parameter.The most attention is given to the problem of determining the behavior of the invariant measure /x£ of the Markov process u\ = (u\(t,-),... ,u^(t,-)) in the space of continuous functions as e -► 0, and also of describing transitions of Uj between stable stationary solutions of nonperturbed systems of PDE.The behavior of p7 and the transitions are defined by large deviations for the field u€(t,x).