Seminario de investigación: DYNAMICS OF STOCHASTIC PDES: A SURVEY, por Tomás Caraballo

El jueves 18 de abril de 2024 a las 12:30 h tendrá lugar el seminario de investigación titulado “Dynamics of stochastic PDEs: a survey”, impartido por Tomás Caraballo, de la Universidad de Sevilla. El seminario será presencial y se impartirá en la Sala de Conferencias de la E.T.S. de Arquitectura. Os animamos a todos a asistir.

ABSTRACT: The aim of this talk is to provide a survey on different aspects related to the dynamics of systems modeled by stochastic partial differential equations. We first report on the dynamics of random dynamical systems generated by stochastic PDE with linear multiplicative or additive noise. The main technique is a conjugation transformation which allows us to obtain a random dynamical system generated by the original stochastic problem. However, when the noise is more general than additive or multiplicative, this transformation does not work, but we still have two other alternatives to handle our problem. The first one consists in approximating the noisy term by a Wong-Zakai approximation (also called colored noise). In this way we can consider a random partial differential equation which generates a random dynamical system and the theory of random dynamical systems can be applied. A reason justifying this approach is that the random dynamical system generated by the Wong-Zakai approximation converges to the random dynamical system generated by the stochastic problem when the noise is additive or multiplicative. However, the convergence for general multiplicative noise is still unsolved. The second approach to analyze the case of nonlinear multiplicative noise is to apply the theory of weak mean random attractor which provides interesting information about the dynamics of the problem in an appropriate phase space.