Consider the following Cauchy problem for the first order quasilinear strictly hy- perbolic system ?u ?u + A(u) = 0, ...Consider the following Cauchy problem for the first order quasilinear strictly hy- perbolic system ?u ?u + A(u) = 0, ?t ?x t = 0 : u = f(x). We let M = sup |f (x)| < +∞. x∈R The main result of this paper is that under the assumption that the system is weakly linearly degenerated, there exists a positive constant ε independent of M, such that the above Cauchy problem admits a unique global C1 solution u = u(t,x) for all t ∈ R, provided that +∞ |f (x)|dx ≤ ε, ?∞ +∞ ε |f(x)|dx ≤ . M∞展开更多
By means of the continuous Glimm functional, a proof is given on the global existence of classical solutions to Cauchy problem for general first order quasilinear hyperbolic systems with small initial total variation.
Calculations of He+H2+ (v=l,j=l) reaction system are carded out on a new potential energy surface (PES) at different collision energies with the quasi-classical trajectory (QCT) method. The results of the reaction pro...Calculations of He+H2+ (v=l,j=l) reaction system are carded out on a new potential energy surface (PES) at different collision energies with the quasi-classical trajectory (QCT) method. The results of the reaction probability and the cross section curves show an obvious oscillatory structure attributed to the resonances caused by the potential well of the Hell2+ complex. The three angular distributions P(θr), P(φr) and P(θr,(φr) as well as four polarization dependent differential cross sections (PDDCSs) are calculated, respectively. Results indicate that the collision energy has great influence on both the vector correlation of k-k', k-j', k-k'-j' and the PDDCSs of the title reaction. The rotational polarization of product Hell+ presents diverse characteristics at dif- ferent collision energies. The rotational angular momentum vectorsj' of product are both aligned and oriented. Furthermore, the product Hell+ tends to scatter forward correspondingly as the collision energy increases.展开更多
Based on the theory of semi-global classical solutions to quasilinear hyperbolic systems, the authors apply a unified constructive method to establish the local exact boundary(null) controllability and the local bound...Based on the theory of semi-global classical solutions to quasilinear hyperbolic systems, the authors apply a unified constructive method to establish the local exact boundary(null) controllability and the local boundary(weak) observability for a coupled system of 1-D quasilinear wave equations with various types of boundary conditions.展开更多
基金Project supported by the National Natural Science Foundation of China (No.10225102) the 973 Project of the Ministry of Science and Technology of China and the Doctoral Programme Foundation of the Ministry of Education of China.
文摘Consider the following Cauchy problem for the first order quasilinear strictly hy- perbolic system ?u ?u + A(u) = 0, ?t ?x t = 0 : u = f(x). We let M = sup |f (x)| < +∞. x∈R The main result of this paper is that under the assumption that the system is weakly linearly degenerated, there exists a positive constant ε independent of M, such that the above Cauchy problem admits a unique global C1 solution u = u(t,x) for all t ∈ R, provided that +∞ |f (x)|dx ≤ ε, ?∞ +∞ ε |f(x)|dx ≤ . M∞
文摘By means of the continuous Glimm functional, a proof is given on the global existence of classical solutions to Cauchy problem for general first order quasilinear hyperbolic systems with small initial total variation.
基金supported by the National Natural Science Foundation of China(Grant Nos. 10504017 and 10874104)the Key Project of Chinese Ministry of Education (Grant No. 206093)
文摘Calculations of He+H2+ (v=l,j=l) reaction system are carded out on a new potential energy surface (PES) at different collision energies with the quasi-classical trajectory (QCT) method. The results of the reaction probability and the cross section curves show an obvious oscillatory structure attributed to the resonances caused by the potential well of the Hell2+ complex. The three angular distributions P(θr), P(φr) and P(θr,(φr) as well as four polarization dependent differential cross sections (PDDCSs) are calculated, respectively. Results indicate that the collision energy has great influence on both the vector correlation of k-k', k-j', k-k'-j' and the PDDCSs of the title reaction. The rotational polarization of product Hell+ presents diverse characteristics at dif- ferent collision energies. The rotational angular momentum vectorsj' of product are both aligned and oriented. Furthermore, the product Hell+ tends to scatter forward correspondingly as the collision energy increases.
文摘Based on the theory of semi-global classical solutions to quasilinear hyperbolic systems, the authors apply a unified constructive method to establish the local exact boundary(null) controllability and the local boundary(weak) observability for a coupled system of 1-D quasilinear wave equations with various types of boundary conditions.
