Xiaokai Huo, KAUST: Relative entropy of compressible model for fluid mixtures
Jan. 10, 3:45pm-4:45pm, DM 409A
The relative entropy method was first developed in the context of hyperbolic system of conservation laws. It provides a measure of the difference between solutions. In this talk, I will show the application of this method in studying the relaxation limit of a multi-species Euler-Korteweg system. I will first show the formal derivation of the limit equations via asymptotic analysis. Then I will derive a relative entropy inequality for the difference between weak solutions to the original system and strong solutions to the approximate system. Finally, I will present the nonlinear estimates using the relative entropy methods and prove the convergence theorem. The relative entropy method provides a nature nonlinear estimate and is the key to obtaining the convergence result.
Nathan Totz, University of Miami
Jan. 31, 3:45pm-4:45pm, DM 409A
Annie Millet, University Paris 1: How stochastic shocks influence a determistic life
Feb. 7, 3:45pm-4:45pm, DM 409A
I will present some results on parabolic or dispersive nonlinear PDEs subject to a random perturbation. This « noise » models the sum of many infinitesimal shocks in the environment. Besides well posedness, some properties of the solution will be discussed, such as discretization schemes, concentration of the distribution when the intensity of the noise approaches 0, long time behaviour.
Pavel Lushnikov, University of New Mexico
March 7, 3:45-4:45pm, DM 409A
Francisco Cala-Rodriguez, Universidad Austral de Chile
March 28, 3:45-4:45pm, DM 409A
Alexander Stokolos, Georgia Southern University
April 11, 3:45-4:45pm, DM 409A