Date: Wed. 24th September at 2PM
Title: Regularisation by noise of quasilinear partial differential equations
Abstract: In these talks, we deal with strong existence and uniqueness for a quasilinear stochastic partial differential equation driven by a two-parameter Brownian white
noise. We restrict ourselves to the case where the diffusion is identity matrix and the drift is a Borel measurable vector field of at most linear growth. Under additional monotonicity condition, we show the existence of a strong solution which is path-by-path unique. This result relies on an extension of Eisenbaum’s local time space formula to the Brownian sheet and a Gronwall type double integral inequality. When the drift is merely bounded we show the existence of a Sobolev differentiable strong solution which is pathwise unique. The result is based on Davie variational techniques. This result extends to the Brownian sheet case those obtained by Zvonkin (1974) and Veretennikov (1979) for one-parameter SDEs.
These talks are based on some recent joint works with Moustapha Dieye, Olivier Menoukeu Pamen and Frank Proske.