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The Prandtl equation introduced by Prandtl in 1904 is a basic equation describling the behavior of the fluid near the boundary at high Reynolds number regime. In this talk, I will first introduce some...
Rossby-Haurwitz waves are an important class of explicit solutions to the incompressible Euler equation on a rotating 2-sphere. We will introduce our recent work on the nonlinear stability of degree-2...
I will give a review of the KP solitons based on Grassmannians. In the talk, I will also give several physical applications of KP solitons to shallow water wave phenomena, and discuss some initial val...
In his pioneering work in 1860, Riemann proposed the Riemann problem and solved it for isentropic gas in terms of shocks and rarefaction waves. It eventually became the foundation of the theory of one...
The formal limit of the one-dimensional Vlasov-Poisson-Landau (VPL) system in the combined small Knudsen and quasineutral regimes gives the compressible Euler system. In the talk I will present a rece...
Incompressible and compressible fluids pose many important mathematical physics problems, which are crucial to understand the practical problems from gas dynamics, weather forecast, ocean waves and th...
Incompressible and compressible fluids pose many important mathematical physics problems, which are crucial to understand the practical problems from gas dynamics, weather forecast, ocean waves and th...
We analyze the refocusing properties of time reversed waves that propagate in two different media during the forward and backward stages of a time-reversal experiment. We consider two regimes of wave ...
A one-dimensional system describing the propagation of low Mach number flames in sprays is studied. We show that pulsating waves may exist when the droplet distribution in the unburnt region is spatia...
We consider systems of reactive Boussinesq equations in two dimensional strips that are not aligned with gravity s direction. We prove that for any width of such strips and for arbitrary Rayleigh and ...
We consider the traveling wave problem for the one dimensional Keller-Segel system with a birth term of either a Fisher/KPP type or with a truncation for small population densities. We prove that ther...
We consider solutions of a scalar reaction-diffusion equation of the ignition type with a random, stationary and ergodic reaction rate. We show that solutions of the Cauchy problem spread with a deter...
We consider the Fisher-KPP equation with a nonlocal saturation effect defined through an interaction kernel φ(x) and investigate the possible differences with the standard Fisher-KPP equation. Our fir...
This paper reviews several mathematical techniques that have been developed to analyze the asymptotic behavior of waves and particles propagating in a heterogeneous medium. The heterogeneous medium is...
Wave propagation in complex media is an ubiquitous phenomenon–applications include light propagation through the atmosphere, underwater acoustic, tomography, and innumerable other ones. These problems...

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