Schedule-at-a-Glance

18 PRIMA 2013 AbstractsKazhikhov-Vaigant model which is a kind of compressibleNavier-Stokes equations with the shear viscosity µ a positiveconstant and the bulk viscosity λ is a power functionof the density.The initial data can be arbitrarily large tocontain vacuum states. This is joint with Yi Wang andZhouping Xin.Global solutions for transonic self-similar twodimensionalRiemann problemsEun Heui KimCalifornia State University, Long Beach, USAEunHeui.Kim@csulb.eduWe discuss the recent development of multi-dimensionaltransonic Riemann problems. More precisely we discussanalytical results and numerical results on a simplifiedmodel system – the nonlinear wave system.Long Time behaviors of the Vlasov-Poisson-Boltzmann EquationsHai-Liang LiCapital Normal University, Chinahailiang.li.math@gmail.comThis talk is concerned with the long time behaviors ofglobal solution to the Vlasov-Poisson-Boltzmann (VPB)equations with binary elastic collision of hard sphere asthe initial data is a small perturbation of the globalMaxwellian. In terms of the spectrum analysis of linearizedsystem and energy estimates, the optimal timedecay rates of global solution is established, and the influenceof electric filed governed by the self-consistent Poissonequation on the distribution of the spectra and thetime-asymptotical behaviors are justified.Traveling waves of chemotaxis modelsTong LiUniversity of Iowa, USAtong-li@uiowa.eduWe study global existence and long time behavior of classicalsolutions for a hyperbolic-parabolic system derivedfrom the Keller-Segel model describing chemotaxis. Weestablish the existence and the nonlinear stability of largeamplitudetraveling wave solutions to the system of nonlinearconservation laws derived from Keller-Segel model.Asymptotic behavior of solutions to Euler-Poisson equations for bipolar hydrodynamicmodel of semiconductorsMing MeiChamplain College Saint-Lambert and McGill University,Canadammei@champlaincollege.qc.ca, ming.mei@mcgill.caIn this talk, we study the Cauchy problem for 1-D Euler-Poisson system, which represents a physically relevanthydrodynamic model but also a challenging case for abipolar semiconductor device by considering two differentpressure functions and a non-flat doping profile. Differentfrom the previous studies for the case with two identicalpressure functions and zero doping profile, we realize thatthe asymptotic profiles of this more physical model aretheir corresponding stationary waves (steady-state solutions)rather than the diffusion waves. Furthermore, weprove that, when the flow is fully subsonic, by means ofa technical energy method with some new development,the smooth solutions of the system are unique, exist globallyand time-algebraically converge to the correspondingstationary solutions. The optimal algebraic convergencerates are obtained.This is a joint work with D. Donatelli, B. Rubino and R.SampalmieriCompressible Navier-Stokes equations withChapman dissipationRonghua PanGeorgia Institute of Technology, USApanrh@math.gatech.eduFrom its physical origin, the viscosity and heat conductivityin compressible fluids depend on absolute temperaturethrough power laws. The mathematical theory onthe well-posedness and regularity on this setting is widelyopen. I will report some recent progress made on thisdirection, with emphasis on the lower bound of temperature,and global existence of solutions in one or multipledimensions. The relation between thermodynamics lawsand Navier-Stokes equations will also be discussed. Thistalk is based on joint works with Weizhe Zhang.Stability of steady state solutions for Euler-Maxwell equationsYue-Jun PengBlaise Pascal University, Francepeng@math.univ-bpclermont.frWe consider Euler-Maxwell equations arising in the modelingof magnetized plasmas. For such equations steadyequilibrium states with zero velocity exist. For small initialdata, we show global existence of smooth solutionswith convergence toward the steady states as the timegoes to infinity. In this problem, the main ingredient isan induction argument on the order of the derivatives ofsolutions in energy estimates. It is also efficient to obtainthe global stability of solutions with exponential decaynear steady states for Euler-Poisson equations.Traveling waves for slow erosionWen ShenPennsylvania State University, USAshen_w@math.psu.eduWe consider an integro-differential equation that describesthe slow erosion of granular flow in one space dimension,{(u t+exp ∫ +∞xu(x, 0) = ū(x).)f(u x(t, y)) dy =0, xHere u(x, t) denotes the height of the standing profileat the point (x, t), and the time variable t denotes theamount of mass that passes through. The function f(u x)is the erosion function, which denotes the rate of erosion(or deposition if negative) per unit mass per distancetravelled. In a normalized model, f(1) = 0, indicating acritical slope u x = 1 where no erosions or depositionsoccur.Due to the nonlinearity of the function f, various typesof singularities will form in the solution u(x, t), includingkinks (jumps in u x) and shocks (jumps in u). Existenceof BV solutions is proved in [4], and semi-group solutionsare established in [2], using a modified form of wave fronttracking approximation. In the simpler case where u xdoes not blow up, uniqueness of solutions is also achieved[1].In this talk we construct particular forms of travelingwave solutions for (1), which connect to x = ±∞ with(1)