the asymptotic behavior of globally smooth solutions of the multidimensional isentropic hydrodynamic model for semiconductors abstract in this paper we study the asymptotic behavior of globally smooth solutions of the cauchy problem for the multidimensional isentropic hydrodynamic model for semiconductors in r d we prove that smooth solutions close to equilibrium of the problem converge to a stationary solution exponentially fast as t

convergence of the fractional step lax friedrichs scheme and godunov scheme for the isentropic system of gas dynamics a convergence theorem of the fractional step lax friedrichs scheme and godunov scheme for an inhomogeneous system of isentropic gas dynamics 1 5 3 is established by using the framework of compensated compactness meanwhile a corresponding existence theorem of global solutions with large data containing the vacuum is obtained

subsonic flow for the multidimensional euler poisson system we establish the existence and stability of subsonic potential flow for the steady euler poisson system in a multidimensional nozzle of a finite length when prescribing the electric potential difference on a non insulated boundary from a fixed point at the exit and prescribing the pressure at the exit of the nozzle the euler poisson system for subsonic potential flow can be reduced to a nonlinear elliptic system of second order in this paper we develop a technique to achieve a priori c 1 alpha estimates of solutions to a quasi linear second order elliptic system with mixed boundary conditions in a multidimensional domain enclosed by a lipschitz continuous boundary in particular we discovered a special structure of the euler poisson system which enables us to obtain c 1 alpha estimates of the velocity potential and the electric potential functions and this leads us to establish structural stability of subsonic flows for the euler poisson system under perturbations of various data

convergence of shock capturing schemes for the compressible euler poisson equations we are concerned with approximate methods to construct global solutions with geometrical structure to the compressible euler poisson equations in several space variables a shock capturing numerical scheme is introduced to overcome the new difficulties from the nonlinear resonance of the system and the nonlocal behavior of the source terms the convergence and consistency of the shock capturing scheme for the equations is proved with the aid of the compensated compactness method then new existence results of the global solutions with geometrical structure are obtained the traces of the weak solutions are defined and then the weak solutions are proved to satisfy the boundary conditions the initial data are arbitrarily large withl bounds

convergence of the viscosity method for isentropic gas dynamics a convergence theorem for the method of artificial viscosity applied to the isentropic equations of gas dynamics is established convergence of a subsequence in the strong topology is proved without uniform estimates on the derivatives using the theory of compensated compactness and an analysis of progressing entropy waves

local in time existence and uniqueness of solutions to the prandtl equations by energy methods we prove local existence and uniqueness for the two dimensional prandtl system in weighted sobolev spaces under oleinik s monotonicity assumption in particular we do not use the crocco transform or any change of variables our proof is based on a new nonlinear energy estimate for the prandtl system this new energy estimate is based on a cancellation property that is valid under the monotonicity assumption to construct the solution we use a regularization of the system that preserves this nonlinear structure this new nonlinear structure may give some insight into the convergence properties from the navier stokes system to the euler system when the viscosity goes to 0 2015 wiley periodicals inc

nonlinear resonance for quasilinear hyperbolic equation the purpose of this paper is to study the wave behavior of hyperbolic conservation laws with a moving source resonance occurs when the speed of the source is too close to one of the characteristic speeds of the system for the nonlinear system characteristic speeds depend on the basic dependence variables and resonance gives rise to nonlinear interactions which lead to rich wave phenomena motivated by physical examples a scalar model is proposed and analyzed to describe the qualitative behavior of waves for a general system in resonance with the source analytical understanding is used to design a numerical scheme based on the random choice method an important physical example is transonic gas flow through a nozzle this analysis provides a transparent and revealing qualitative understanding of wave behavior of gas flow including such phenomena as nonlinear stability instability and changing types of waves

global smooth solutions to the multidimensional hydrodynamic model for plasmas with insulating boundary conditions the existence of global smooth solutions to the multidimensional hydrodynamic model for plasmas of electrons and positively charged ions with insulating boundary conditions is shown under the assumption that the initial densities are close to a constant furthermore it is proved that the particle densities converge exponentially fast to the constant steady state

refinements of stochastic domination in a recent paper by two of the authors the concepts of upwards and downwards epsilon movability were introduced mainly as a technical tool for studying dynamical percolation of interacting particle systems in this paper we further explore these concepts which can be seen as refinements or quantifications of stochastic domination and we relate them to previously studied concepts such as uniform insertion tolerance and extractability

symmetrical prandtl boundary layer expansions of steady navier stokes equations on bounded domain abstract this paper is concerned with the validity of the prandtl boundary layer theory in the inviscid limit of the steady incompressible navier stokes equations which is an extension of the pioneer paper 13 y guo et al 2017 ann pde from a domain of 0 l r to 0 l 0 2 under the symmetry assumption we establish the validity of the prandtl boundary layer expansions and the error estimates the convergence rate as e 0 is also given

thresholds in three dimensional restricted euler poisson equations abstract this work provides a description of the critical threshold phenomenon in multi dimensional restricted euler poisson rep equations introduced in h liu e tadmor spectral dynamics of the velocity gradient field in restricted fluid flows comm math phys 228 2002 435 466 for three dimensional rep equations we identified both upper thresholds for the finite time blow up of solutions and subthresholds for the global existence of solutions with the thresholds depending on the relative size of the eigenvalues of the initial velocity gradient matrix and the initial density for the attractive forcing case these one sided threshold conditions of the initial configurations are optimal and the corresponding results also hold for arbitrary n dimensions n 3

stability of steady states of the compressible euler poisson system in r 3 abstract we investigate the global existence and asymptotic behavior of smooth solutions near a non flat steady state to the compressible euler poisson system in r 3 using some concise energy estimates and an interpolation trick we refine the global existence and show that the solution converges to the stationary solution exponentially fast we assume that the h 3 norms of the initial density and velocity are small but the higher derivatives can be arbitrarily large in this sense our method simplifies the proof of hsiao et al 2003 17 and improves the results of it

stability of steady state solutions for an isentropic hydrodynamic model of semiconductors of two species abstract we discuss the stability of the steady state solutions for an isentropic hydrodynamic model of semiconductors of two species we consider not only the mass and momentum equations for electrons but also those two equations for holes the recombination effects between electrons and holes are taken into consideration as well we study the case where the doping profile is close to zero and depends on the spacial variable x we shall show that steady state solutions are asymptotically stable

weak solutions to a hydrodynamic model for semiconductors and relaxation to the drift diffusion equation we investigate the relaxation problem for the hydrodynamic isentropic euler poisson system when the momentum relaxation time tends to zero very sharp estimates on the solutions independent of the relaxation time are obtained and used to establish compactness

global existence and asymptotic behavior for a multidimensional nonisentropic hydrodynamic semiconductor model with the heat source abstract in this paper a multidimensional nonisentropic hydrodynamic model for semiconductors with the nonconstant lattice temperature is studied the model is self consistent in the sense that the electric field which forms a forcing term in the momentum equation is determined by the coupled poisson equation global existence to the cauchy problem for the multidimensional nonisentropic hydrodynamic semiconductor model with the small perturbed initial data is established and the asymptotic behavior of these smooth solutions is investigated namely that the solutions converge to the general steady state solution exponentially fast as t is obtained moreover the existence and uniqueness of the stationary solutions are investigated

convergence of the godunov scheme for a simplified one dimensional hydrodynamic model for semiconductor devices convergence of approximate solutions derived by the godunov scheme for a simplified one dimensional hydrodynamic model for semiconductor devices is established by using the compensated compactness method a global existence theorem is shown and a numerical method for the computation of the physical global solution of this model is provided by this approach

kinetic formulation of the isentropic gas dynamics and p systems we consider the 2 x 2 hyperbolic system of isentropic gas dynamics in both eulerian or lagrangian variables also called the p system we show that they can be reformulated as a kinetic equation using an additional kinetic variable such a formulation was first obtained by the authors in the case of multidimensio nal scalar conservation laws a new phenomenon occurs here namely that the advection velocity is now a combination of the macroscopic and kinetic velocities various applications are given we recover the invariant regions deduce new l estimates using moments lemma and prove l w stability for 7 3

global solutions to the compressible euler equations with geometrical structure we prove the existence of global solutions to the euler equations of compressible isentropic gas dynamics with geometrical structure including transonic nozzle flow and spherically symmetric flow due to the presence of the geometrical source terms the existence results themselves are new especially as they pertain to radial flow in an unbounded region vec x geqq 1 and to transonic nozzle flow arbitrary data withl bounds are allowed in these results a shock capturing numerical scheme is introduced to compute such flows and to construct approximate solutions the convergence and consistency of the approximate solutions generated from this scheme to the global solutions are proved with the aid of a compensated compactness framework

asymptotic convergence to planar stationary waves for multi dimensional unipolar hydrodynamic model of semiconductors abstract in this study we consider the high dimensional unipolar hydrodynamic model for semiconductors in the form of euler poisson equations based on the results that we have obtained in the first part huang et al 2011 16 for the 1 d case we can further show the stability of planar stationary waves in multi dimensional case utilizing the energy method we obtain the global existence of the solutions of high dimensional euler poisson equations for the unipolar hydrodynamic model and prove that the solutions converge to the planar stationary waves time exponentially

a viscous approximation for a 2 d steady semiconductor or transonic gas dynamic flow existence theorem for potential flow in this paper we solve a boundary value problem in a two dimensional domain 1 for a system of equations of fluid poisson type that is a viscous approximation to a potential equation for the velocity coupled with an ordinary differential equation along the streamlines for the density and a poisson equation for the electric field a particular case of this system is a viscous approximation of transonic flow models the general case is a model for semiconductors we show existence of a density p velocity potential cp and electric potential in the bounded domain r that are c fi c fi and w2 p 2 functions respectively such that p cp 3 the speed ivlpl and the electric field e v are uniformly bounded in the viscous parameter this is a necessary step in the existing programs in order to show existence of a solution for the transonic flow problem 0 19 john wiley sons inc 1 presentation of the model

global solutions to the isothermal euler poisson system with arbitrarily large data abstract we prove the global existence of a solution to the euler poisson system with arbitrarily large data in a one dimensional geometry the pressure law we consider is deduced from an isothermal assumption for the electrons gas in this case nishida has already pointed out that the linear part of the glimm functional is decreasing with respect to time using a glimm scheme he used this property to construct globally defined weak solutions for the euler system with arbitrary large data we follow his outline of proof here a new difficulty arises with the source term due to the electric field a key point is that the glimm scheme is almost conservative this quasi conservation of charge leads to a uniform estimate of the total variation of the electric field this estimate allows to prove the convergence of the scheme