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
In this paper, oscillation of solutions to a class of impulsive delay parabolic partial differential equations system with higher order Laplace operator is studied. Under two different boundary value conditions, we es...In this paper, oscillation of solutions to a class of impulsive delay parabolic partial differential equations system with higher order Laplace operator is studied. Under two different boundary value conditions, we establish some sufficient criteria with respect to the oscillations of such systems, employing first-order impulsive delay differential inequalities. The results fully reflect the influence action of impulsive and delay in oscillation.展开更多
In this paper, we study the oscillation of solutions to the systems of impulsive neutral delay parabolic partial differential equations. Under two different boundary conditions, we obtain some sufficient conditions fo...In this paper, we study the oscillation of solutions to the systems of impulsive neutral delay parabolic partial differential equations. Under two different boundary conditions, we obtain some sufficient conditions for oscillation of all solutions to the systems.展开更多
This paper is devoted to the study of the vortex dynamics of the Cauchy problem for a parabolic Ginzburg Landau system which simulates inhomogeneous type II superconducting materials and three-dimensional superconduct...This paper is devoted to the study of the vortex dynamics of the Cauchy problem for a parabolic Ginzburg Landau system which simulates inhomogeneous type II superconducting materials and three-dimensional superconducting thin films having variable thickness. We will prove that the vortex of the problem is moved by a codimension k mean curvature flow with external force field. Besides, we will show that the mean curvature flow depends strongly on the external force, having completely different phenomena from the usual mean curvature flow.展开更多
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the Natural Science Foundation of Hunan Province under Grant 05JJ40008.
文摘In this paper, oscillation of solutions to a class of impulsive delay parabolic partial differential equations system with higher order Laplace operator is studied. Under two different boundary value conditions, we establish some sufficient criteria with respect to the oscillations of such systems, employing first-order impulsive delay differential inequalities. The results fully reflect the influence action of impulsive and delay in oscillation.
基金Supported by the National Natural Science Foundation of China(10471086).
文摘In this paper, we study the oscillation of solutions to the systems of impulsive neutral delay parabolic partial differential equations. Under two different boundary conditions, we obtain some sufficient conditions for oscillation of all solutions to the systems.
基金Supported by National 973-Project and Basic Research Grant of Tsinghua University
文摘This paper is devoted to the study of the vortex dynamics of the Cauchy problem for a parabolic Ginzburg Landau system which simulates inhomogeneous type II superconducting materials and three-dimensional superconducting thin films having variable thickness. We will prove that the vortex of the problem is moved by a codimension k mean curvature flow with external force field. Besides, we will show that the mean curvature flow depends strongly on the external force, having completely different phenomena from the usual mean curvature flow.
