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A Mini-Course on Degenerate Nonlinear Parabolic-Hyperbolic Equations with Stochastic Force (6)
时间  Datetime
2018-05-25 09:30 — 11:30 
地点  Venue
1106, Math Building
报告人  Speaker
Hermano Frid
单位  Affiliation
IMPA, Brazil
邀请人  Host
Yachun Li
报告摘要  Abstract

The plan is to make a detailed account of recent results on stochastic degenerate parabolic-hyperbolic equations. Basically, the paper by A. Debussche, M. Hofmanová and J. Vovelle, published in The Annals of Probability, 144, no. 3 (2016), 1916-1955, and the paper by C. Bauzet, G. Vallet and P. Wittbold, in JHDE, 12, no. 3 (2015), 501-533. The same groups have also wrote papers on the hyperbolic case, some results of which they use in the parabolic-hyperbolic case so we will need to know also the hyperbolic counterpart. In order to understand these works one needs to know well stochastic integration, properties of the stochastic  integral, including the so called Burkholder-Daves-Gundy inequality, which is useful in this context. That means, a good deal of the mini course will be consumed introducing these objects, which normally would require not only the basics of probability, but the theory of continuous time Martingales, Brownian motion, stochastic integration, Martingale inequalities, etc. On the other hand, it goes without saying, to understand these works one needs to be familiar with the deterministic theory of nonlinear degenerate parabolic-hyperbolic equations. We do not assume the students are conversant with the latter, but we do hope that the attendance will have already been introduced to the basics of this theory. We will keep the focus on the papers mentioned and try to cut a diagonal in order to introduce and give the main properties of whatever is necessary for the understanding of the papers.