Ming Mei

Asymptotic stability of travelling waves for Nicholson's blowflies equation with diffusion

This paper considers the nonlinear stability oftravelling wavefronts of a time-delayed diffusive Nicholson blowflies equation. We prove that, under a weighted L 2 norm, ifa solution is sufficiently close to a travelling wave front initially, it converges exponentially to the wavefront as t → ∞. The rate ofconvergence is also estimated.

GLOBAL STABILITY OF MONOSTABLE TRAVELING WAVES FOR NONLOCAL TIME-DELAYED REACTION-DIFFUSION EQUATIONS ∗

For a class of nonlocal time-delayed reaction-diffusion equations, we prove that all noncritical wavefronts are globally exponentially stable, and critical wavefronts are globally algebraically stable when the initial perturbations around the wavefront decay to zero exponentially near the negative infinity regardless of the magnitude of time delay. This work also improves and develops the existing stability results for local and nonlocal reaction-diffusion equations with delays. Our approach is based on the combination of the weighted energy method and the Green function technique.

Asymptotic behaviour of solutions of the hydrodynamic model of semiconductors

Degond and Markowich discussed the existence and uniqueness of a steady-state solution in the subsonic case for the one-dimensional hydrodynamic model of semiconductors. In the present paper, we reconsider the existence and uniqueness of a globally smooth subsonic steady-state solution, and prove its stability for small perturbation. The proof method we adopt in this paper is based on elementary energy estimates.

Stability of strong travelling waves for a non-local time-delayed reaction-diffusion equation

The paper is concerned with a non-local time-delayed reaction–diffusion equation. We prove the (time) asymptotic stability of a travelling wavefront without a smallness assumption on its wavelength, i.e. the so-called strong wavefront, by means of the (technical) weighted energy method, when the initial perturbation around the wave is small. The exponential convergent rate is also given. Selection of a suitable weight plays a key role in the proof.

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

In this paper, we study the n-dimensional (

Exponential Stability of Nonmonotone Traveling Waves for Nicholson's Blowflies Equation

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

CONVERGENCE RATES TO TRAVELLING WAVES FOR A NONCONVEX RELAXATION MODEL

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

Analysis on the critical speed of traveling waves

L^\infty