Description
Probability and Statistics seminar.
Speaker: Vivek Kumar.
Affiliation: IIT Roorkee.
Date and Time: Tuesday 27 August, 12:05 pm - 1:05 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Existence and uniqueness of solutions of generalised stochastic
Burger equation perturbed by Volterra noise.
Abstract:
In this article, we investigate the existence and uniqueness of local mild solutions for the one-dimensional generalized stochastic Burgers equation (GSBE) containing a non-linearity of polynomial type and perturbed by α-regular cylindrical Volterra
process and having Dirichlet boundary conditions. The Banach fixed point theorem (or
contraction mapping principle) is used to obtain the local solvability results. The L∞-
estimate on both time and space for the stochastic convolution involving the α-regular
cylindrical Volterra process is obtained. Further, the existence and uniqueness of global
mild solution of GSBE up to third order nonlinearity is shown.
2010 Mathematics Subject Classification. Primary: 60H15, 60G22; Secondary: 35Q35,
35R60.
Key-words: Stochastic Burgers equation, Volterra process, γ-Radonifying operator,
Stopping time.