In this paper,we study systems of conservation laws in one space dimension.We prove that for classical solutions in Sobolev spaces H^(s),with s>3/2,the data-to-solution map is not uniformly continuous.Our results a...In this paper,we study systems of conservation laws in one space dimension.We prove that for classical solutions in Sobolev spaces H^(s),with s>3/2,the data-to-solution map is not uniformly continuous.Our results apply to all nonlinear scalar conservation laws and to nonlinear hyperbolic systems of two equations.展开更多
A 2D finite element model was established for inertia friction welding of GH4169 nickel-base superalloy based on the ABAQUS environment.The remeshing and map solution techniques were adopted to solve the problem of el...A 2D finite element model was established for inertia friction welding of GH4169 nickel-base superalloy based on the ABAQUS environment.The remeshing and map solution techniques were adopted to solve the problem of element distortion.The effect of rotation speed on the temperature field and axial shortening of joints was investigated.The results show that the interface temperature increases rapidly to higher than 900℃within 1s.And then,it increases slowly to a quasi-stable value.The axial shortening begins to augment quickly when a uniform interface temperature field has formed and the plasticized material is extruded from the interface to form an obvious flash.The rotation speed of the flywheel controls the welding process and has a significant influence on the temperature evolution and axial shortening of joints.展开更多
We provide sufficient conditions for the existence and multiplicity of periodic solutions for Duffing's equations with jumping nonlinearities under resonance conditions.
We introduce a generalized numerical algorithm to construct the solution landscape,which is a pathway map consisting of all the stationary points and their connections.Based on the high-index optimizationbased shrinki...We introduce a generalized numerical algorithm to construct the solution landscape,which is a pathway map consisting of all the stationary points and their connections.Based on the high-index optimizationbased shrinking dimer(Hi OSD)method for gradient systems,a generalized high-index saddle dynamics(GHi SD)is proposed to compute any-index saddles of dynamical systems.Linear stability of the index-k saddle point can be proved for the GHi SD system.A combination of the downward search algorithm and the upward search algorithm is applied to systematically construct the solution landscape,which not only provides a powerful and efficient way to compute multiple solutions without tuning initial guesses,but also reveals the relationships between different solutions.Numerical examples,including a three-dimensional example and the phase field model,demonstrate the novel concept of the solution landscape by showing the connected pathway maps.展开更多
A new Lax matrix is introduced for the integrable symplectic map (ISM), and the non-dynamical(i. e. constant) r-matrix of ISM is obtained. Moreover, an effective approach is systematically presented to construct the e...A new Lax matrix is introduced for the integrable symplectic map (ISM), and the non-dynamical(i. e. constant) r-matrix of ISM is obtained. Moreover, an effective approach is systematically presented to construct the explicit solution(here, the explicit solution means algebraic-geometric solution expressed by the Riemann-Theta function) of a soliton system or nonlinear evolution equation from Lax matrix, r-matrix, and the theory of nonlinearization through taking the Toda lattice as an example. The given algebraic-geometric solution of the Toda lattice is almost-periodic and includes the periodic and finite-band solution.展开更多
This note considers the solution to the generalized Sylvester matrix equation AV ＋ BW = VF with F being an arbitrary matrix, where V and W are the matrices to be determined. With the help of the Kronecker map, an exp...This note considers the solution to the generalized Sylvester matrix equation AV ＋ BW = VF with F being an arbitrary matrix, where V and W are the matrices to be determined. With the help of the Kronecker map, an explicit parametric solution to this matrix equation is established. The proposed solution possesses a very simple and neat form, and allows the matrix F to be undetermined.展开更多
We investigate a parabolic-elliptic system which is related to a harmonic map from a compact Riemann surface with a smooth boundary into a Lorentzian manifold with a warped product metric.We prove that there exists a ...We investigate a parabolic-elliptic system which is related to a harmonic map from a compact Riemann surface with a smooth boundary into a Lorentzian manifold with a warped product metric.We prove that there exists a unique global weak solution for this system which is regular except for at most finitely many singular points.展开更多
文摘In this paper,we study systems of conservation laws in one space dimension.We prove that for classical solutions in Sobolev spaces H^(s),with s>3/2,the data-to-solution map is not uniformly continuous.Our results apply to all nonlinear scalar conservation laws and to nonlinear hyperbolic systems of two equations.
基金the National Natural Science Foundation of China(No.51005180)the Ao-Xiang Star Project of NPU(Northwestern Polytechnical University)+2 种基金the Research Fund of the State Key Laboratory of Solidification Processing(NPU,China)(No.69-QP- 2011)the Program for New Century Excellent Talents in University by the Ministry of Education of China (No.NECT-08-0463)the 111 Project(No.B08040)
文摘A 2D finite element model was established for inertia friction welding of GH4169 nickel-base superalloy based on the ABAQUS environment.The remeshing and map solution techniques were adopted to solve the problem of element distortion.The effect of rotation speed on the temperature field and axial shortening of joints was investigated.The results show that the interface temperature increases rapidly to higher than 900℃within 1s.And then,it increases slowly to a quasi-stable value.The axial shortening begins to augment quickly when a uniform interface temperature field has formed and the plasticized material is extruded from the interface to form an obvious flash.The rotation speed of the flywheel controls the welding process and has a significant influence on the temperature evolution and axial shortening of joints.
基金Supported by the Natural Science Foundation of China(10001025)the Natural Science Foundation of Beijing(1022003)the Foundation of Beijing Educational Committee
文摘We provide sufficient conditions for the existence and multiplicity of periodic solutions for Duffing's equations with jumping nonlinearities under resonance conditions.
基金supported by National Natural Science Foundation of China(Grant No.11861130351)the support from the Elite Program of Computational and Applied Mathematics for Ph D Candidates of Peking University。
文摘We introduce a generalized numerical algorithm to construct the solution landscape,which is a pathway map consisting of all the stationary points and their connections.Based on the high-index optimizationbased shrinking dimer(Hi OSD)method for gradient systems,a generalized high-index saddle dynamics(GHi SD)is proposed to compute any-index saddles of dynamical systems.Linear stability of the index-k saddle point can be proved for the GHi SD system.A combination of the downward search algorithm and the upward search algorithm is applied to systematically construct the solution landscape,which not only provides a powerful and efficient way to compute multiple solutions without tuning initial guesses,but also reveals the relationships between different solutions.Numerical examples,including a three-dimensional example and the phase field model,demonstrate the novel concept of the solution landscape by showing the connected pathway maps.
文摘A new Lax matrix is introduced for the integrable symplectic map (ISM), and the non-dynamical(i. e. constant) r-matrix of ISM is obtained. Moreover, an effective approach is systematically presented to construct the explicit solution(here, the explicit solution means algebraic-geometric solution expressed by the Riemann-Theta function) of a soliton system or nonlinear evolution equation from Lax matrix, r-matrix, and the theory of nonlinearization through taking the Toda lattice as an example. The given algebraic-geometric solution of the Toda lattice is almost-periodic and includes the periodic and finite-band solution.
基金the National Natural Science Foundation of China (No.60374024)the Program for Changjiang Scholars and Innovative Research Team in University
文摘This note considers the solution to the generalized Sylvester matrix equation AV ＋ BW = VF with F being an arbitrary matrix, where V and W are the matrices to be determined. With the help of the Kronecker map, an explicit parametric solution to this matrix equation is established. The proposed solution possesses a very simple and neat form, and allows the matrix F to be undetermined.
基金supported by National Natural Science Foundation of China(Grant Nos.11471014 and 11471299)the Fundamental Research Funds for the Central Universities
文摘We investigate a parabolic-elliptic system which is related to a harmonic map from a compact Riemann surface with a smooth boundary into a Lorentzian manifold with a warped product metric.We prove that there exists a unique global weak solution for this system which is regular except for at most finitely many singular points.
