In this paper, we are concerned with the solvability for a class of nonlinear sequential fractional dynamical systems with damping infinite dimensional spaces, which involves fractional Riemann-Liouville derivatives. ...In this paper, we are concerned with the solvability for a class of nonlinear sequential fractional dynamical systems with damping infinite dimensional spaces, which involves fractional Riemann-Liouville derivatives. The solutions of the dynamical systems are obtained by utilizing the method of Laplace transform technique and are based on the formula of the Laplace transform of the Mittag-Leffler function in two parameters. Next, we present the existence and uniqueness of solutions for nonlinear sequential fractional dynamical systems with damping by using fixed point theorems under some appropriate conditions.展开更多
The initial boundary value problem for a Kirchhoff equation with Lipschitz type continuous coefficient is studied on bounded domain.Under some conditions,the energy decaying and blow-up of solution are discussed.By re...The initial boundary value problem for a Kirchhoff equation with Lipschitz type continuous coefficient is studied on bounded domain.Under some conditions,the energy decaying and blow-up of solution are discussed.By refining method,the exponent decay estimates of the energy function and the estimates of the life span of blow-up solutions are given.展开更多
In this paper we investigate optimal control problems governed by a advection-diffusion-reaction equation. We present a method for deriving conditions in the form of Pontryagin’s principle. The main tools used are th...In this paper we investigate optimal control problems governed by a advection-diffusion-reaction equation. We present a method for deriving conditions in the form of Pontryagin’s principle. The main tools used are the Ekeland’s variational principle combined with penalization and spike variation techniques.展开更多
This paper is devoted to a class of inverse coefficient problems for nonlinear elliptic hemivariational inequalities. The unknown coefficient of elliptic hemivariational inequalities depends on the gradient of the sol...This paper is devoted to a class of inverse coefficient problems for nonlinear elliptic hemivariational inequalities. The unknown coefficient of elliptic hemivariational inequalities depends on the gradient of the solution and belongs to a set of admissible coefficients. It is shown that the nonlinear elliptic hemivariational inequalities are uniquely solvable for the given class of coefficients. The result of existence of quasisolutions of the inverse problems is obtained.展开更多
文摘In this paper, we are concerned with the solvability for a class of nonlinear sequential fractional dynamical systems with damping infinite dimensional spaces, which involves fractional Riemann-Liouville derivatives. The solutions of the dynamical systems are obtained by utilizing the method of Laplace transform technique and are based on the formula of the Laplace transform of the Mittag-Leffler function in two parameters. Next, we present the existence and uniqueness of solutions for nonlinear sequential fractional dynamical systems with damping by using fixed point theorems under some appropriate conditions.
基金the Natural Science Foundation of Hunan Province (No.05jj40008)the Youth-items Research Fund of Hengyang Normal University (No.08A27)
文摘The initial boundary value problem for a Kirchhoff equation with Lipschitz type continuous coefficient is studied on bounded domain.Under some conditions,the energy decaying and blow-up of solution are discussed.By refining method,the exponent decay estimates of the energy function and the estimates of the life span of blow-up solutions are given.
文摘In this paper we investigate optimal control problems governed by a advection-diffusion-reaction equation. We present a method for deriving conditions in the form of Pontryagin’s principle. The main tools used are the Ekeland’s variational principle combined with penalization and spike variation techniques.
基金supported by the National Natural Science Foundation of China(No.10971019)the GuangxiProvincial Natural Science Foundation of China(No.2010GXNSFA013114)
文摘This paper is devoted to a class of inverse coefficient problems for nonlinear elliptic hemivariational inequalities. The unknown coefficient of elliptic hemivariational inequalities depends on the gradient of the solution and belongs to a set of admissible coefficients. It is shown that the nonlinear elliptic hemivariational inequalities are uniquely solvable for the given class of coefficients. The result of existence of quasisolutions of the inverse problems is obtained.
