The soliton solutions with a double spectral parameter for the principal chiral field are derived by Darboux transformation. The asymptotic behavior of the solutions as time tends to infinity is obtained and the speed...The soliton solutions with a double spectral parameter for the principal chiral field are derived by Darboux transformation. The asymptotic behavior of the solutions as time tends to infinity is obtained and the speeds of the peaks in the asymptotic solutions are not constants.展开更多
In this paper, the Nagumo theorem and the fixed-point theorem are used to prove the existence and the uniqueness and to estimate the asymptotic expansion of the shock solutions of the boundary value problems for a cla...In this paper, the Nagumo theorem and the fixed-point theorem are used to prove the existence and the uniqueness and to estimate the asymptotic expansion of the shock solutions of the boundary value problems for a class of quasilinear differential equations, the asymptotic expansion of solution of any orders including boundary is obtained.展开更多
In this paper,the author considers a class of complete noncompact Riemannian manifoldswhich satisfy certain conditions on Ricci curvature and volume comparison. It is shown thatany harmonic map with finite energy from...In this paper,the author considers a class of complete noncompact Riemannian manifoldswhich satisfy certain conditions on Ricci curvature and volume comparison. It is shown thatany harmonic map with finite energy from such a manifold M into a normal geodesic ball inanother manifold N must be asymptotically constant at the infinity of each large end of M. Arelated existence theorem for harmonic maps is established.展开更多
This paper continues the discussion in [5], and proves the existence of local solution to the problem of interaction of shock and gradient wave. The author uses Newton’s iteration scheme to constructs a sequence of a...This paper continues the discussion in [5], and proves the existence of local solution to the problem of interaction of shock and gradient wave. The author uses Newton’s iteration scheme to constructs a sequence of approximate solutions. By using delicate energy method the convergence of the sequence is eatablished and then it leads to the existence of the genuine solution. The main point of the energy method applied here is first to estimate a linear combination of the approximate solution and the function describing the characteristics of the system, before estimating these two elements separately. The method plays a key role, because it can aviod the smoothness loss caused by the characteristic boundary in the process of interation.展开更多
文摘The soliton solutions with a double spectral parameter for the principal chiral field are derived by Darboux transformation. The asymptotic behavior of the solutions as time tends to infinity is obtained and the speeds of the peaks in the asymptotic solutions are not constants.
文摘In this paper, the Nagumo theorem and the fixed-point theorem are used to prove the existence and the uniqueness and to estimate the asymptotic expansion of the shock solutions of the boundary value problems for a class of quasilinear differential equations, the asymptotic expansion of solution of any orders including boundary is obtained.
文摘In this paper,the author considers a class of complete noncompact Riemannian manifoldswhich satisfy certain conditions on Ricci curvature and volume comparison. It is shown thatany harmonic map with finite energy from such a manifold M into a normal geodesic ball inanother manifold N must be asymptotically constant at the infinity of each large end of M. Arelated existence theorem for harmonic maps is established.
文摘This paper continues the discussion in [5], and proves the existence of local solution to the problem of interaction of shock and gradient wave. The author uses Newton’s iteration scheme to constructs a sequence of approximate solutions. By using delicate energy method the convergence of the sequence is eatablished and then it leads to the existence of the genuine solution. The main point of the energy method applied here is first to estimate a linear combination of the approximate solution and the function describing the characteristics of the system, before estimating these two elements separately. The method plays a key role, because it can aviod the smoothness loss caused by the characteristic boundary in the process of interation.
