Existence of Multiple Equilibrium Points in Global Attractor for the Strongly Damped Wave Equations

The aim of this paper is to study the long-term behavior of strongly damped wave equations with a Lyapunov function. Using the theory established by estimating the Z2 index of some sets and the idea of invariant sets of semi-flow,the properties of the global attractor for strongly damped wave equation are discussed. The existence of multiple equilibrium points in global attractor for strongly damped wave equations with critical growth of nonlinearity is obtained. And under some additional condition, the infinite dimension of the attractor is proven.

The Global Attractors for the Higher-Order Kirchhoff-Type Equation with Nonlinear Strongly Damped Term

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 (H1) - (H4). 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.

On the Strongly Damped Wave Equations with Critical Nonlinearities

We study the strongly damped wave equations with critical nonlinearities. By choosing suitable state spaces, we prove sectorial property of the operator matrix together with its adjoint operator, investigate the associated interpolation and extrapolation spaces, analysis the criticality of the nonlinearity with critical growth, and study the higher spatial regularity of the Y-regular solution by bootstrapping.

Superheavy fragments produced in the asymmetric strongly damped collision

The strongly damped collisions of very heavy nuclei ^232Th＋^250Cf at the energy range of 680--1880 MeV have been studied within the improved quantum molecular dynamics model. The production probability of primary superheavy fragments with Z≥ 114 （SHFs） for the asymmetric reaction ^232Th＋^250cf is higher than that for the symmetric reaction ^244Pu＋^244pu and ^238U＋^238U. The calculated results show that the mass and charge distributions of primary fragments, the excitation energy distribution of SHFs depend on the incident energies strongly. Two stages of the decay process of composite systems are distinguished by very different decay slopes, which imply different decay mechanisms of the composite system. The first stage is for the decay of giant composite systems and the second one corresponds to the decay of fragments of giant composite systems including SHFs through emitting neutron, proton or other charged particles, and also through fission or fragmentation. The slow reduction of SHFs in the second stage seems to be helpful for the survival of primary superheavy fragments.

Mixed Spectral and Pseudospectral Methods for a Nonlinear Strongly Damped Wave Equation in an Exterior Domain

The aim of this paper is to develop the mixed spectral and pseudospectral methods for nonlinear problems outside a disc,using Fourier and generalized Laguerre functions.As an example,we consider a nonlinear strongly damped wave equation.The mixed spectral and pseudospectral schemes are proposed.The convergence is proved.Numerical results demonstrate the efficiency of this approach.

GLOBAL SOLUTIONS AND FINITE TIME BLOW UP FOR DAMPED KLEIN-GORDON EQUATION

We study the Cauchy problem of strongly damped Klein-Gordon equation. Global existence and asymptotic behavior of solutions with initial data in the potential well are derived. Moreover, not only does finite time blow up with initial data in the unstable set is proved, but also blow up results with arbitrary positive initial energy are obtained.

Global Attractor for a Class of Nonlinear Generalized Kirchhoff-Boussinesq Model

In this paper, we study the long time behavior of solution to the initial boundary value problem for a class of Kirchhoff-Boussinesq model flow . We first prove the wellness of the solutions. Then we establish the existence of global attractor.

GLOBAL EXISTENCE, UNIFORM DECAY AND EXPONENTIAL GROWTH FOR A CLASS OF SEMI-LINEAR WAVE EQUATION WITH STRONG DAMPING

In this paper, we consider the nonlinearly damped semi-linear wave equation associated with initial and Dirichlet boundary conditions. We prove the existence of a local weak solution and introduce a family of potential wells and discuss the invariants and vacuum isolating behavior of solutions. Furthermore, we prove the global existence of solutions in both cases which are polynomial and exponential decay in the energy space respectively, and the asymptotic behavior of solutions for the cases of potential well family with 0 〈 E（0） 〈 d. At last we show that the energy will grow up as an exponential function as time goes to infinity, provided the initial data is large enough or E（0） 〈 0.

Study on the formation of the composite system of ^(238)U+^(238)U

Strongly damped reactions of 238U+238U, at Ecm = 680—1880 MeV have been studied based on the improved quantum molecular dynamics model. We find that at a certain energy region the entrance channel potential is weakly repulsive and the dissipation is very strong after touching configuration, these two effects make the time delay of re-separation for colliding system. The single particle potential well of the transiently formed composite system has Coulomb barrier about 15—20 MeV high at the surface, which makes the excited unbound protons being still embedded in the potential well and moving in a common mono-single particle potential for a period of time and thus restrains from quick decay of the composite system.