In this paper, a spectral method to analyze the generalized Benjamin Bona Mahony equations is used. The existence and uniqueness of global smooth solution of these equations are proved. The large time error estimati...In this paper, a spectral method to analyze the generalized Benjamin Bona Mahony equations is used. The existence and uniqueness of global smooth solution of these equations are proved. The large time error estimation between the spectral approximate solution and the exact solution is obtained.展开更多
The Boussinesq approximation ,where the viscosity depends polynomially on the shear rate ,finds more and more frequent use in geological practice,In this paper ,we consider the periodic initial value problem and inita...The Boussinesq approximation ,where the viscosity depends polynomially on the shear rate ,finds more and more frequent use in geological practice,In this paper ,we consider the periodic initial value problem and inital value problem for this modified Boussinesq approximation with the viscous part of the stress tensor T^v=τ(e)-μ1△e,where the nonlinear function τ(e) satisfies τij(e)eij≥C|e|^p or τij(e)eij ≥C(|e|^2+|e|^p).The existence,uniqueness and regulartiy of the weak solution is proved for p> 2n/(n+2).展开更多
In this paper, we consider the asymptotic behavior of solutions for a class of nonclassical diffusion equation. We show the squeezing property and the existence of exponential attractor for this equation. We also make...In this paper, we consider the asymptotic behavior of solutions for a class of nonclassical diffusion equation. We show the squeezing property and the existence of exponential attractor for this equation. We also make the estimates on its fractal dimension and exponential attraction.展开更多
This paper deals with the asymptotic behaviour of solutions for thegeneralized symmetric regularized long wave equations with dissipation term. We first show theexistence of global weak attractors for the periodic ini...This paper deals with the asymptotic behaviour of solutions for thegeneralized symmetric regularized long wave equations with dissipation term. We first show theexistence of global weak attractors for the periodic initial value problem of this equations in H^2x H^1. And then by an energy equation and an idea of Ghidaglia and Guo, we conclude that the globalweak attractor is actually the global strong attractor for S(t) in H^2 (Ω) x H^1 (Ω). The finitedimensionality of the global attractor is also established.展开更多
文摘In this paper, a spectral method to analyze the generalized Benjamin Bona Mahony equations is used. The existence and uniqueness of global smooth solution of these equations are proved. The large time error estimation between the spectral approximate solution and the exact solution is obtained.
文摘The Boussinesq approximation ,where the viscosity depends polynomially on the shear rate ,finds more and more frequent use in geological practice,In this paper ,we consider the periodic initial value problem and inital value problem for this modified Boussinesq approximation with the viscous part of the stress tensor T^v=τ(e)-μ1△e,where the nonlinear function τ(e) satisfies τij(e)eij≥C|e|^p or τij(e)eij ≥C(|e|^2+|e|^p).The existence,uniqueness and regulartiy of the weak solution is proved for p> 2n/(n+2).
文摘In this paper, we consider the asymptotic behavior of solutions for a class of nonclassical diffusion equation. We show the squeezing property and the existence of exponential attractor for this equation. We also make the estimates on its fractal dimension and exponential attraction.
基金This research is supported by the National Natural Science Foundation of China(Grant 10271034).
文摘This paper deals with the asymptotic behaviour of solutions for thegeneralized symmetric regularized long wave equations with dissipation term. We first show theexistence of global weak attractors for the periodic initial value problem of this equations in H^2x H^1. And then by an energy equation and an idea of Ghidaglia and Guo, we conclude that the globalweak attractor is actually the global strong attractor for S(t) in H^2 (Ω) x H^1 (Ω). The finitedimensionality of the global attractor is also established.
