On some regularized nonlinear hyperbolic equations

Abstract: It is known that the solutions of nonlinear hyperbolic partial differential equations develop discontinuous shocks in finite time even with smooth initial data. Those shock are problematic in the theoretical study and in the numerical computations. To avoid these shocks, many regularizations have been studied in the literature. For example, adding diffusion and/or dispersion to the equation. In this talk, we present and study some non-diffusive and non-dispersive regularizations of the Burgers equation and the barotropic Euler equations that have similar properties as the classical equations.

analysis of PDEsclassical analysis and ODEsfunctional analysisprobabilityspectral theory

Audience: researchers in the discipline

Quebec Analysis and Related Fields Graduate Seminar