0 Introduction We consider the orbital instability of standing waves for the Klein-Gordon-Zakharov system with different propagation speeds in three space
We study a fourth order curve flow, which is the gradient flow of a functional describing the shapes of human red blood cells. We prove that for any smooth closed initial curve in ?2, the flow has a smooth solution fo...We study a fourth order curve flow, which is the gradient flow of a functional describing the shapes of human red blood cells. We prove that for any smooth closed initial curve in ?2, the flow has a smooth solution for all time and the solution subconverges to a critical point of the functional.展开更多
In this paper, we use the abstract theory of semilinear parabolic equations and a priori estimate techniques to prove the global existence and uniqueness of smooth solutions to the Cauchy problem for the following sys...In this paper, we use the abstract theory of semilinear parabolic equations and a priori estimate techniques to prove the global existence and uniqueness of smooth solutions to the Cauchy problem for the following system of parabolic equations. ψ<sub>t</sub>=-（σ-α）ψ-σθ<sub>x</sub>-αψ<sub>xx</sub> θ<sub>t</sub>=-（1-β）θ-vψ<sub>x</sub>（ψθ）-βθ<sub>xx</sub>展开更多
We formulate a class of functionals in space forms such that its critical points include the r-minimal hyper-surface and the minimal hyper-surface as special cases. We obtain the algebraic, differential and variationa...We formulate a class of functionals in space forms such that its critical points include the r-minimal hyper-surface and the minimal hyper-surface as special cases. We obtain the algebraic, differential and variational characteristics of the critical surfaces determined by the critical points. We prove the Simons' type nonexistence theorem which indicates that in the unit sphere, there exists no stable critical surfaces, and the Alexandrov's type existence theorem which indicates that in Euclidean space, the sphere is the only stable critical surfaces.展开更多
The authors study the large-time behaviour of global smooth solutions to initial-boundary value problems for the system of one-dimensional nonlinear thermoviscoelasticity. It is found that the solution may possess pha...The authors study the large-time behaviour of global smooth solutions to initial-boundary value problems for the system of one-dimensional nonlinear thermoviscoelasticity. It is found that the solution may possess phase transition phenomena when the material is not monotone, and the solution may decay to a stable state for the monotone case.展开更多
基金This work is supported by NSFC(No．10771151 and No．10726034)Sichuan Youth Sciences and Technology Foundation(No．07ZQ026-009)the Morningside Center．
文摘0 Introduction We consider the orbital instability of standing waves for the Klein-Gordon-Zakharov system with different propagation speeds in three space
基金supported by Postdoctoral Science Foundation of China, National Natural Science Foundationof China (No. 10631020, 10871061)the Grant for PhD Program of Ministry of Education of China
文摘We study a fourth order curve flow, which is the gradient flow of a functional describing the shapes of human red blood cells. We prove that for any smooth closed initial curve in ?2, the flow has a smooth solution for all time and the solution subconverges to a critical point of the functional.
文摘In this paper, we use the abstract theory of semilinear parabolic equations and a priori estimate techniques to prove the global existence and uniqueness of smooth solutions to the Cauchy problem for the following system of parabolic equations. ψ<sub>t</sub>=-（σ-α）ψ-σθ<sub>x</sub>-αψ<sub>xx</sub> θ<sub>t</sub>=-（1-β）θ-vψ<sub>x</sub>（ψθ）-βθ<sub>xx</sub>
基金supported by National Natural Science Foundation of China (Grant No.10871061)
文摘We formulate a class of functionals in space forms such that its critical points include the r-minimal hyper-surface and the minimal hyper-surface as special cases. We obtain the algebraic, differential and variational characteristics of the critical surfaces determined by the critical points. We prove the Simons' type nonexistence theorem which indicates that in the unit sphere, there exists no stable critical surfaces, and the Alexandrov's type existence theorem which indicates that in Euclidean space, the sphere is the only stable critical surfaces.
文摘The authors study the large-time behaviour of global smooth solutions to initial-boundary value problems for the system of one-dimensional nonlinear thermoviscoelasticity. It is found that the solution may possess phase transition phenomena when the material is not monotone, and the solution may decay to a stable state for the monotone case.
