Vorträge in der Woche 02.11.2009 bis 08.11.2009

Montag, 02.11.2009: Stochastic geometric wave equations with values in compact Riemannian homogeneous spaces

Zdzislaw Brzezniak

Abstract: Let M be a compact Riemannian homogeneous space (e.g. a Euclidean sphere). We prove existence of a global weak solution of the stochastic wave equation mathbf D t partial tu sum k 1 d mathbf D x k partial x k u J u lambda 0(u) partial tu sum k 1 d lambda k(u) partial x k u ) , dot W where J is a continuous tangent vector field on M , lambda i:TM to TM are continuous replace such that lambda i(p):T pM to T pM is linear for every p in M vector bundles homomorphisms , W is a spatially homogeneous Wiener process on mathbb R d with finite spectral measure and d ge 1 . A new general method of constructing weak solutions of SPDEs, that does not rely on martingale representation theorem, is used. This talk is based on joint works with M. Ondrej 'at from Prague.