Skip to main navigationSkip to main content
The University of Southampton
Mathematical Sciences

Finite-time blow-up of a non-local stochastic parabolic problem arising in shear banding formation in metals Seminar

Time:
12:00
Date:
10 November 2015
Venue:
54/7033 (7C)

Event details

Applied Mathematics Seminar

In the current work we investigate the behaviour of a non-local stochastic parabolic problem. We first prove the local-in-time existence and uniqueness of a weak solution. Then we check the extendability in time of the weak solution. In particular, the rest of paper is devoted to the investigation of the conditions under which finite-time blow-up occurs. We first prove that noise term induced finite-time blow up takes place when the stochastic term is rather big independently of the size of the non-local term. Afterwards, non-local-term induced finite-time blow occurs when the nonlinearity satisfies some specific growth conditions. In this case some fundamental results like maximum principle and Hopf's type lemma in the context of SPDEs are first provided and later Kaplan's eigenfunction method adjusted to the our non-local SPDE is employed.

Speaker information

Nikos Kavallaris, University of Chester. Senior Lecturer

Privacy Settings