Bin Wu

Extinction and Decay Estimates of Solutions for a Class of Porous Medium Equations

The extinction phenomenon of solutions for the homogeneous Dirichlet boundary value problem of the porous medium equation, is studied. Sufficient conditions about the extinction and decay estimates of solutions are obtained by using-integral model estimate methods and two crucial lemmas on differential inequality.

Determination of an unknown source for a thermoelastic system with a memory effect

We study an inverse problem of determining a spatially varying source term in a thermoelastic medium with a memory effect. The coupling phenomena between elasticity and heat as well as the memory effect make such an inverse problem very complicated. We firstly prove a pointwise Carleman estimate for a general strongly coupled hyperbolic system, and then obtain a Carleman estimate for the hyperbolic thermoelastic system. Based on this estimate, we finally establish a Holder stability for the inverse source problem only by making a displacement measurement on a given subdomain for sufficiently large times, provided the source be known near the boundary. The uniqueness for such an inverse problem is yielded as a direct result.

Conditional stability and uniqueness for determining two coefficients in a hyperbolic–parabolic system

We study the inverse problem of determining two spatially varying coefficients in a thermoelastic model with the following observation data: displacement in a subdomain ω satisfying ∂ω⊃∂Ω along a sufficiently large time interval, both displacement and temperature at a suitable time over the whole spatial domain. Based on a Carleman estimate on the hyperbolic–parabolic system, we prove the Lipschitz stability and the uniqueness for this inverse problem under some a priori information.

Global Existence and Extinction of Weak Solutions to a Class of Semiconductor Equations with Fast Diffusion Terms

We consider the transient drift-diffusion model with fast diffusion terms. This problem is not only degenerate but also singular. We first present existence result for general nonlinear diffusivities for the Dirichlet-Neumann mixed boundary value problem. Then, the extinction phenomenon of weak solutions for the homogeneous Dirichlet boundary problem is studied. Sufficient conditions on the extinction and decay estimates of solutions are obtained by using -integral model estimate method.

Existence of Weak Solutions to a Class of Degenerate Semiconductor Equations Modeling Avalanche Generation

We consider the drift-diffusion model with avalanche generation for evolution in time of electron and hole densities 𝑛, 𝑝 coupled with the electrostatic potential 𝜓 in a semiconductor device. We also assume that the diffusion term is degenerate. The existence of local weak solutions to this Dirichlet-Neumann mixed boundary value problem is obtained.