Quasilinear stochastic cauchy problem in abstract colombeau spaces

Abstract

Generalized solutions to the abstract Cauchy problem for a quasilinear equation with the generator of an integrated semigroup and with terms reflecting nonlinear perturbations and white noise type perturbations are under consideration. An abstract stochastic Colombeau algebra is constructed, and solutions in the algebra are studied. Copyright © 2012 Irina V. Melnikova and Uljana A. Alekseeva.