American Institute of Mathematical Sciences

In this paper, we consider a viscoelastic Kirchhoff equation with Balakrishnan-Taylor damping, dynamic boundary conditions and a time-varying delay term acting on the boundary. By using the Faedo-Galerkin approximation method, we first prove the well-posedness of the solutions. By introducing suitable energy and perturbed Lyapunov functionals, we then prove the general decay results, from which the usual exponential and polynomial decay rates are only special cases. To achieve these results, we consider the following two cases according to the coefficient α of the strong damping term: for the presence of the strong damping term (α>0), we use the strong damping term to control the time-varying delay term, under a restriction of the size between the time-varying delay term and the strong damping term; for the absence of the strong damping term (α=0), we use the viscoelasticity term to control the time-varying delay term, under a restriction of the size between the time-varying delay term and the kernel function.

We study the time evolution of the three dimensional Vlasov-Poisson plasma interacting with a positive point charge in the case of infinite mass. We prove the existence and uniqueness of the classical solution to the system by assuming that the initial density slightly decays in space, but not integrable. This result extends a previous theorem for Yukawa potential obtained in [10] to the case of Coulomb interaction.

In cloud computing environment, in order to optimize the deployment scheduling of resources, it is necessary to improve the accuracy of the optimal solution, guarantee the convergence ability of the algorithm, and improve the performance of cloud computing. In this paper, a multi-objective optimization algorithm based on improved particle swarm is proposed. A multi-objective optimization model is built. Improved multi-scale particle swarm is used to optimize the built multi-objective model. The combination of the global search capability and the local search capability of the algorithm is realized by using Gaussian variation operator with varied scales. The large scale Gaussian variation operator with concussion characteristics can complete fast global search for decision space, so that particles can quickly locate the surrounding area of the optimal solution, which enhances the ability to escape the local optimal solution of the algorithm and avoids the occurrence of precocious convergence. The small scale variation operator gradually reduces the area near the optimal solution. Experimental results show that the improved particle swarm optimization algorithm can effectively improve the precision of the optimal solution and ensure the convergence of the algorithm.

In this paper, we consider a composite DC optimization problem with a cone-convex system in locally convex Hausdorff topological vector spaces. By using the properties of the epigraph of the conjugate functions, some necessary and sufficient conditions which characterize the strong Fenchel-Lagrange duality and the stable strong Fenchel-Lagrange duality are given. We apply the results obtained to study the minmax optimization problem and $l_1$ penalty problem.