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On the long-time behaviour of a semilinear stochastic partial differential equation

GFM seminar
FCUL, C6, room 6.2.33
2017-06-14 11:00 .. 12:00
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by Marco Dozzi (Inst. Elie Cartan, Univ. de Lorraine, Nancy)

We consider stochastic equations of the prototype

$$du(t, x) = (Δu(t, x) + γu(t, x) + u(t, x)^{1+β})dt + κu(t, x)dB_t$$

on a smooth domain $$D ⊂ \mathbb{R}^d$$ with Dirichlet boundary condition and non-negative initial condition, where $$β > 0$$, γ and κ are constants and $$(B_t, t ≧ 0)$$ is a real-valued brownian motion or fractional brownian motion with Hurst parameter $$H > 1/2$$. By means of an associated random partial differential equation we estimate the blowup time of the solution $$u$$. In the case of brownian motion we estimate the probability for the existence of a non trivial positive global solution.

This is joint work with J.-A. Lopez-Mimbela and E. Kolkovska at CIMAT (Guanajuato, Mexico).