Feimin Huang

CONVERGENCE OF VISCOSITY SOLUTIONS FOR ISOTHERMAL GAS DYNAMICS

We study the hyperbolic system of Euler equations for an isothermal, compressible fluid. The strong convergence theorem of approximate solutions is proved by the theory of compensated compactness. The existence of a weak entropy solution to Cauchy problems with large

Large Time Behavior of Solutions to n-Dimensional Bipolar Hydrodynamic Models for Semiconductors

L^\infty

Weak Solution to Pressureless Type System

initial data which may include a vacuum is also obtained. We note that we establish the commutation relations not only for the weak entropies but also for the strong ones by using the analytic extension theorem.

Hydrodynamic Limit of the Boltzmann Equation with Contact Discontinuities

In this paper, we study the n-dimensional (

The limit of the boltzmann equation to the euler equations for riemann problems

n\geq1

Long-time Behavior of Solutions to the Bipolar Hydrodynamic Model of Semiconductors with Boundary Effect

) bipolar hydrodynamic model for semiconductors in the form of Euler–Poisson equations. In the 1-D case, when the difference between the initial electron mass and the initial hole mass is nonzero (switch-on case), the stability of nonlinear diffusion waves has been open for a long time. In order to overcome this difficulty, we ingeniously construct some new correction functions to delete the gaps between the original solutions and the diffusion waves in

ASYMPTOTIC CONVERGENCE TO STATIONARY WAVES FOR UNIPOLAR HYDRODYNAMIC MODEL OF SEMICONDUCTORS

L^2

Subsonic-Sonic Limit of Approximate Solutions to Multidimensional Steady Euler Equations

-space, so that we can deal with the 1-D case for general perturbations, and prove the

Zero dissipation limit to rarefaction wave with vacuum for one-dimensional compressible Navier-Stokes equations

L^\infty

Emergence of bi-cluster flocking for the Cucker–Smale model

-stability of diffusion waves in the 1-D case. The optimal convergence rates are also obtained. Furthermore, based on the 1-D results, we establish some crucial energy estimates and apply a new but key inequality to prove the stability of planar diffusion waves in n-D case. This is the first result for the multidimensional bipolar hydrodynamic model of semiconductors.