Date: Thursday, April 05, 2018
Location: 1360 East Hall (3:00 PM to 4:00 PM)
Title: Branching particles representation for nonlinear Cauchy problems
Abstract: We provide a probabilistic representations of the solution of some semilinear hyperbolic and high-order PDEs based on branching diffusions. This is a direct extension of our previous work in the context of semilinear parabolic PDEs based on the classical Mc Kean representation for KPP equations. These representations pave the way for a Monte-Carlo approximation of the solution, thus bypassing the curse of dimensionality. We illustrate the numerical implications in the context of some popular PDEs in physics such as nonlinear Klein-Gordon equation, a simplified scalar version of the Yang-Mills equation, a fourth-order nonlinear beam equation and the Gross- Pitaevskii PDE as an example of nonlinear Schrodinger equations.
Sponsored by the Van Eenam Lecture Series
Files: 4975_Michigan-05042018-Lect3.pdf
Speaker: Nizar Touzi
Institution: Ecole Polytechniqie
Event Organizer: Erhan Bayraktar math-events@umich.edu
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