The numerical simulation is based on the authors' high-order models with a dissipative term for nonlinear and dispersive wave in water of varying depth. Corresponding finite-difference equations and general condit...The numerical simulation is based on the authors' high-order models with a dissipative term for nonlinear and dispersive wave in water of varying depth. Corresponding finite-difference equations and general conditions for open and fixed natural boundaries with an arbitrary reflection coefficient and phase shift are also given in this paper. The systematical tests of numerical simulation show that the theoretical models, the finite-difference algorithms and the boundary conditions can give good calculation results for the wave propagating in shallow and deep water with an arbitrary slope varying from gentle to steep.展开更多
This paper deals with the blow-up rate estimates of positive solutions for systems of heat equationswith nonlinear boundary conditions. The upper and lower bounds of blow-up rate are obtained.
In this note, the long-time behavior of solutions for the following parabolic systemsare studied, where Ω is a bounded smooth domain, v is the outer normal vector on Ω.u<sub>n</sub>,.B<sub>n</su...In this note, the long-time behavior of solutions for the following parabolic systemsare studied, where Ω is a bounded smooth domain, v is the outer normal vector on Ω.u<sub>n</sub>,.B<sub>n</sub>∈C<sup>1</sup>（Ω） and satisfy u<sub>0</sub>/v<sub>0</sub> = u<sub>0</sub><sup>m</sup>v<sub>0</sub><sup>n</sup>, v<sub>0</sub>/v = u<sub>0</sub><sup>p</sup>v<sub>0</sub><sup>q</sup>, x∈Ω;and u<sub>0</sub>（x）】0, v<sub>0</sub>（x）】0, x∈Ω.m,n,p. q are nonnegative constants. Our main result reads as follows.Theorem. Solutions of （1） exist globally展开更多
In this paper we consider the periodic solutions of nonlinear parabolic systems with nonlinear boundary conditions.By constructing the Poincare operator,we obtain the existence of W<sub>p</sub><sup>2...In this paper we consider the periodic solutions of nonlinear parabolic systems with nonlinear boundary conditions.By constructing the Poincare operator,we obtain the existence of W<sub>p</sub><sup>2β</sup>-periodic weak solutions under some reasonable assumptions.展开更多
This paper deals with the blowup estimates near the blowup time for the system of heat equations in a half space coupled through nonlinear boundary conditions. The upper and lower bounds of blowup rate are established...This paper deals with the blowup estimates near the blowup time for the system of heat equations in a half space coupled through nonlinear boundary conditions. The upper and lower bounds of blowup rate are established. The uniqueness and nonuniqueness results for the system with vanishing initial value are given.展开更多
Returning to moon has become a top topic recently. Many studies have shown that soft landing is a challenging problem in lunar exploration. The lunar soft landing in this paper begins from a 100 km circular lunar park...Returning to moon has become a top topic recently. Many studies have shown that soft landing is a challenging problem in lunar exploration. The lunar soft landing in this paper begins from a 100 km circular lunar parking orbit. Once the landing area has been selected and it is time to deorbit for landing, a ΔV burn of 19.4 m/s is performed to establish a 100×15 km elliptical orbit. At perilune, the landing jets are ignited, and a propulsive landing is performed. A guidance and control scheme for lunar soft landing is proposed in the paper, which combines optimal theory with nonlinear neuro-control. Basically, an optimal nonlinear control law based on artificial neural network is presented, on the basis of the optimum trajectory from perilune to lunar surface in terms of Pontryagin's maximum principle according to the terminal boundary conditions and performance index. Therefore some optimal control laws can be carried out in the soft landing system due to the nonlinear mapping function of the neural network. The feasibility and validity of the control laws are verified in a simulation experiment.展开更多
The following reaction diffusion systemsare discussed, where is a bounded domain with smooth boundaryis small. Let ,where I is the unit matrix. It can be proved that solution exists globally if and only if all the pri...The following reaction diffusion systemsare discussed, where is a bounded domain with smooth boundaryis small. Let ,where I is the unit matrix. It can be proved that solution exists globally if and only if all the principal minors of A have nonnegative determinants.展开更多
文摘The numerical simulation is based on the authors' high-order models with a dissipative term for nonlinear and dispersive wave in water of varying depth. Corresponding finite-difference equations and general conditions for open and fixed natural boundaries with an arbitrary reflection coefficient and phase shift are also given in this paper. The systematical tests of numerical simulation show that the theoretical models, the finite-difference algorithms and the boundary conditions can give good calculation results for the wave propagating in shallow and deep water with an arbitrary slope varying from gentle to steep.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 19831060) and "333" Project of Jiangsu Province.
文摘This paper deals with the blow-up rate estimates of positive solutions for systems of heat equationswith nonlinear boundary conditions. The upper and lower bounds of blow-up rate are obtained.
基金Project supported by the National Natural Science Foundation of China.
文摘In this note, the long-time behavior of solutions for the following parabolic systemsare studied, where Ω is a bounded smooth domain, v is the outer normal vector on Ω.u<sub>n</sub>,.B<sub>n</sub>∈C<sup>1</sup>（Ω） and satisfy u<sub>0</sub>/v<sub>0</sub> = u<sub>0</sub><sup>m</sup>v<sub>0</sub><sup>n</sup>, v<sub>0</sub>/v = u<sub>0</sub><sup>p</sup>v<sub>0</sub><sup>q</sup>, x∈Ω;and u<sub>0</sub>（x）】0, v<sub>0</sub>（x）】0, x∈Ω.m,n,p. q are nonnegative constants. Our main result reads as follows.Theorem. Solutions of （1） exist globally
文摘In this paper we consider the periodic solutions of nonlinear parabolic systems with nonlinear boundary conditions.By constructing the Poincare operator,we obtain the existence of W<sub>p</sub><sup>2β</sup>-periodic weak solutions under some reasonable assumptions.
基金This work was supported by the National Natural Science Foundation of China(Grant No.10171088)and also by SRF for ROCS,SEM.
文摘This paper deals with the blowup estimates near the blowup time for the system of heat equations in a half space coupled through nonlinear boundary conditions. The upper and lower bounds of blowup rate are established. The uniqueness and nonuniqueness results for the system with vanishing initial value are given.
文摘Returning to moon has become a top topic recently. Many studies have shown that soft landing is a challenging problem in lunar exploration. The lunar soft landing in this paper begins from a 100 km circular lunar parking orbit. Once the landing area has been selected and it is time to deorbit for landing, a ΔV burn of 19.4 m/s is performed to establish a 100×15 km elliptical orbit. At perilune, the landing jets are ignited, and a propulsive landing is performed. A guidance and control scheme for lunar soft landing is proposed in the paper, which combines optimal theory with nonlinear neuro-control. Basically, an optimal nonlinear control law based on artificial neural network is presented, on the basis of the optimum trajectory from perilune to lunar surface in terms of Pontryagin's maximum principle according to the terminal boundary conditions and performance index. Therefore some optimal control laws can be carried out in the soft landing system due to the nonlinear mapping function of the neural network. The feasibility and validity of the control laws are verified in a simulation experiment.
基金Project supported by the National Natural Science Foundation of Chinathe Natural Science Foundation of Jiangsu Province.
文摘The following reaction diffusion systemsare discussed, where is a bounded domain with smooth boundaryis small. Let ,where I is the unit matrix. It can be proved that solution exists globally if and only if all the principal minors of A have nonnegative determinants.
