主 题: Unbounded Positive Solutions of Some Nonlinear Stochastic Parabolic Equations
报告人: Prof. Pao-Liu Chow （Department of Mathematics, Wayne State University, USA）
时 间: 2012-10-17 16:00-17:00
地 点: 理科一号楼1479
The talk is concerned with unbounded solutions of some semi-linear parabolic equations
perturbed by a multiplicative Gaussian white-noise random field. Such equations
arise, for example, from turbulent diffusion and population dynamics in a random
environment. In particular we are mainly interested in the possible existence of
a positive explosive solution, that is, it will become unbounded in finite time in some
sense. To this end we first prove that, under some suitable conditions, a stochastic
parabolic equation can have a positive solution. Next, without the positivity
conditions, we shall provide a set of sufficient conditions for explosion with positive
probability based on the Lyapunov function type of technique. In the case of positive
solutions, it is possible to obtain more explicit conditions for explosion. Assume that
the positivity condtions hold and the nonlinear term is convex, among some other
auxiliary conditions. It will be shown that there exists a positive solution which will
explode either with positive probability or in the mean
