In the paper, the null interior controllability for a fourth order parabolic equation is obtained. The method is based on Lebeau-Rabbiano inequality which is a quantitative unique continuation property for the sum of ...In the paper, the null interior controllability for a fourth order parabolic equation is obtained. The method is based on Lebeau-Rabbiano inequality which is a quantitative unique continuation property for the sum of eigenfunctions of the Laplacian.展开更多
In this paper, we present two second-order numerical schemes to solve the fourth order parabolic equation derived from a diffuse interface model with Peng-Robinson Equation of state （EOS） for pure substance. The mas...In this paper, we present two second-order numerical schemes to solve the fourth order parabolic equation derived from a diffuse interface model with Peng-Robinson Equation of state （EOS） for pure substance. The mass conservation, energy decay property, unique solvability and L~ convergence of these two schemes are proved. Numerical results demon- strate the good approximation of the fourth order equation and confirm reliability of these two schemes.展开更多
A fourth order parabolic system, the bipolar quantum drift-diffusion model in semiconductor simulation, with physically motivated Dirichlet-Neumann boundary condition is studied in this paper. By semidiscretization in...A fourth order parabolic system, the bipolar quantum drift-diffusion model in semiconductor simulation, with physically motivated Dirichlet-Neumann boundary condition is studied in this paper. By semidiscretization in time and compactness argument, the global existence and semiclassical limit are obtained, in which semiclassieal limit describes the relation between quantum and classical drift-diffusion models, Furthermore, in the case of constant doping, we prove the weak solution exponentially approaches its constant steady state as time increases to infinity.展开更多
This paper studies the existence, semiclassical limit, and long-time behavior of weak solutions to the unipolar isentropic quantum drift-diffusion model, a fourth order parabolic system. Semi-discretization in time an...This paper studies the existence, semiclassical limit, and long-time behavior of weak solutions to the unipolar isentropic quantum drift-diffusion model, a fourth order parabolic system. Semi-discretization in time and entropy estimates give the global existence and semiclassical limit of nonnegative weak solutions to the one-dimensional model with a nonnegative large initial value and a Dirichlet-Neumann boundary condition. Furthermore, the weak solutions are proven to exponentially approach constant steady state as time increases to infinity.展开更多
基金Supported by the National Natural Science Foundation of China (Grant Nos. 10671040, 10831007, 10801041)the National Excellent Doctoral Dissertation of China (Grant No. 200522)the New Century Excellent Talents in University (Grant No. 06-0359)
文摘In the paper, the null interior controllability for a fourth order parabolic equation is obtained. The method is based on Lebeau-Rabbiano inequality which is a quantitative unique continuation property for the sum of eigenfunctions of the Laplacian.
文摘In this paper, we present two second-order numerical schemes to solve the fourth order parabolic equation derived from a diffuse interface model with Peng-Robinson Equation of state （EOS） for pure substance. The mass conservation, energy decay property, unique solvability and L~ convergence of these two schemes are proved. Numerical results demon- strate the good approximation of the fourth order equation and confirm reliability of these two schemes.
基金Supported by the Natural Science Foundation of China （No. 10571101, No. 10626030 and No. 10871112）
文摘A fourth order parabolic system, the bipolar quantum drift-diffusion model in semiconductor simulation, with physically motivated Dirichlet-Neumann boundary condition is studied in this paper. By semidiscretization in time and compactness argument, the global existence and semiclassical limit are obtained, in which semiclassieal limit describes the relation between quantum and classical drift-diffusion models, Furthermore, in the case of constant doping, we prove the weak solution exponentially approaches its constant steady state as time increases to infinity.
基金the National Natural Science Foundation of China(No. 10401019)
文摘This paper studies the existence, semiclassical limit, and long-time behavior of weak solutions to the unipolar isentropic quantum drift-diffusion model, a fourth order parabolic system. Semi-discretization in time and entropy estimates give the global existence and semiclassical limit of nonnegative weak solutions to the one-dimensional model with a nonnegative large initial value and a Dirichlet-Neumann boundary condition. Furthermore, the weak solutions are proven to exponentially approach constant steady state as time increases to infinity.
