In this paper, we are going to consider the initial value problem with periodic boundarycondition and the Cauchy problem associated with the system of ferromagnetic chain withthe Gilbert damping term Z_t=-εZ×(Z&...In this paper, we are going to consider the initial value problem with periodic boundarycondition and the Cauchy problem associated with the system of ferromagnetic chain withthe Gilbert damping term Z_t=-εZ×(Z×Z_(zz)+Z×Z_(zz), (ε≥0).The existence of a unique smooth solution is established by using the technique of spatialdifference and crucial a priori estimates of higher-order derivatives in Sobolev spaces.展开更多
In this paper, we study the longtime behavior of solution to the initial boundary value problem for a class of strongly damped Higher-order Kirchhoff type equations: . At first, we prove the existence and uniqueness o...In this paper, we study the longtime behavior of solution to the initial boundary value problem for a class of strongly damped Higher-order Kirchhoff type equations: . At first, we prove the existence and uniqueness of the solution by priori estimation and the Galerkin method. Then, we obtain to the existence of the global attractor. At last, we consider that the estimation of the upper bounds of Hausdorff and fractal dimensions for the global attractors are obtained.展开更多
Using the method of upper and lower solutions and its associated monotone iterative, consider the existence and uniqueness of solution of an initial value problem for the nonlinear fractional diffusion equation.
We investigate the global well-posedness and the global attractors of the solutions for the Higher-order Kirchhoff-type wave equation with nonlinear strongly damping: . For strong nonlinear damping σ and ?, we make a...We investigate the global well-posedness and the global attractors of the solutions for the Higher-order Kirchhoff-type wave equation with nonlinear strongly damping: . For strong nonlinear damping σ and ?, we make assumptions (H<sub>1</sub>) - (H<sub>4</sub>). Under of the proper assume, the main results are existence and uniqueness of the solution in proved by Galerkin method, and deal with the global attractors.展开更多
基金Project supported by the National Natural Science Foundation of China.
文摘In this paper, we are going to consider the initial value problem with periodic boundarycondition and the Cauchy problem associated with the system of ferromagnetic chain withthe Gilbert damping term Z_t=-εZ×(Z×Z_(zz)+Z×Z_(zz), (ε≥0).The existence of a unique smooth solution is established by using the technique of spatialdifference and crucial a priori estimates of higher-order derivatives in Sobolev spaces.
文摘In this paper, we study the longtime behavior of solution to the initial boundary value problem for a class of strongly damped Higher-order Kirchhoff type equations: . At first, we prove the existence and uniqueness of the solution by priori estimation and the Galerkin method. Then, we obtain to the existence of the global attractor. At last, we consider that the estimation of the upper bounds of Hausdorff and fractal dimensions for the global attractors are obtained.
文摘Using the method of upper and lower solutions and its associated monotone iterative, consider the existence and uniqueness of solution of an initial value problem for the nonlinear fractional diffusion equation.
文摘We investigate the global well-posedness and the global attractors of the solutions for the Higher-order Kirchhoff-type wave equation with nonlinear strongly damping: . For strong nonlinear damping σ and ?, we make assumptions (H<sub>1</sub>) - (H<sub>4</sub>). Under of the proper assume, the main results are existence and uniqueness of the solution in proved by Galerkin method, and deal with the global attractors.
