PERIODIC BOUNDARY VALUE PROBLEM AND CAUCHY PROBLEM OF THE GENERALIZED CUBIC DOUBLE DISPERSION EQUATION

In this article, the existence, uniqueness and regularities of the global generalized solution and global classical solution for the periodic boundary value problem and the Cauchy problem of the general cubic double dispersion equationutt - uxx - auxxtt ＋ bux4 - duxxt = f（u）xxare proved, and the sufficient conditions of blow-up of the solutions for the Cauchy problems in finite time are given.

The Family of Global Attractors for Kirchhoff-Type Coupled Equations

This paper mainly studies the initial value problems of Kirchhoff-type coupled equations. Firstly, by giving the hypothesis of Kirchhoff stress term , the Galerkin’s method obtains the existence uniqueness of the overall solution of the above problem by using a priori estimates in the spaces of E0 and Ek, and secondly, it proves that there is a family of global attractors for the above problem, and finally estimates the Hausdorff dimension and the Fractal dimension of the family of global attractors.

Global existence of real roots and random Newton flow algorithm for nonlinear system of equations To memorize Qin's method for 770 anniversaries

To solve nonlinear system of equation,F(x) = 0,a continuous Newton flow x_t(t) = V(x) =-(DF(x))^(-1)F(x),x(0) =x^0 and its mathematical properties,such as the central field,global existence and uniqueness of real roots and the structure of the singular surface,are studied.We concisely introduce random Newton flow algorithm(NFA) for finding all roots,based on discrete Newton flow x^(j+1)=x^j+hV{x^j) with random initial value x^0 and h∈(0,1],and three computable quantities,g_j,d_j and K_j.The numerical experiments with dimension n=300 are provided.

Global well-posedness and time-decay estimates for compressible Navier-Stokes equations with reaction diffusion

We consider the full compressible Navier-Stokes equations with reaction diffusion.A global existence and uniqueness result of the strong solution is established for the Cauchy problem when the initial data is in a neighborhood of a trivially stationary solution.The appearance of the difference between energy gained and energy lost due to the reaction is a new feature for the flow and brings new difficulties.To handle these,we construct a new linearized system in terms of a combination of the solutions.Moreover,some optimal timedecay estimates of the solutions are derived when the initial perturbation is additionally bounded in L1.It is worth noticing that there is no decay loss for the highest-order spatial derivatives of the solution so that the long time behavior for the hyperbolic-parabolic system is exactly the same as that for the heat equation.As a byproduct,the above time-decay estimate at the highest order is also valid for compressible Navier-Stokes equations.The proof is accomplished by virtue of Fourier theory and a new observation for cancellation of a low-medium-frequency quantity.

THE INITIAL BOUNDARY VALUE PROBLEM FOR QUASI-LINEAR SCHRODINGER-POISSON EQUATIONS

In this article, the author studies the iuitial （Dirichlet.） boundary problem for a high field version of the Schroedinger-Poisson equations, which include a nonlinear term in the Poisson equation corresponding to a field-dependent dielectric constant and an effective potential in the Schroedinger equations on the unit cube. h global existence and uniqueness is established for a solution to this problem.

PERIODIC BOUNDARY VALUE PROBLEM OF QUASILINEAR SYSTEM

The existence and uniqueness results about quasilinear periodic boundary value problems are established by using the global inverse function theorem and the result about the existence and uniquencess of periodic solutions for the periodic boundary value problem of nonhomogeneous linear periodic system.