ON STOCHASTIC QUASILINEAR EVOLUTION EQUATIONS IN HILBERT SPACES

Abstract

In this paper, the existence and uniqueness of local mild solution to quasilinear equation with additive cylindrical Wiener process in a separable Hilbert space are established using contraction mapping principle. Here we employ the technique used by Pazy to treat homogeneous quasilinear evolution equations. We first show the existence of mild solution of the corresponding linear part, using which we define a contraction map on a suitable complete metric space. The fixed point then obtained using contraction mapping principle is the mild solution of the quasilinear equation.