Landau-Lifshitz方程的群不变解和守恒律

利用经典李群方法得到了Landau-Lifshitz方程不变群的无穷小生成元,验证其对换位运算构成一个七维的李代数,得到了对应的群不变解,建立了Landau-Lifshit,z新解和旧解之间的关系.同时利用对称和共轭方程组求得了Landau-Lifshitz方程的守恒律.     

The Kolmogorov Operator Associated to a Burgers SPDE in Spaces of Continuous Functions

We are concerned with a viscous Burgers equation forced by a perturbation of white noise type. We study the corresponding transition semigroup in a space of continuous functions weighted by a proper potential, and we show that the infinitesimal generator is the closure (with respect to a suitable topology) of the Kolmogorov operator associated to the stochastic equation. In the last part of the paper we use this result to solve the corresponding Fokker-Planck equation.     

The computation of the adjoint generator for a singular neutral equation

We compute the adjoint generator for the infinitesimal generator A of a C₀-semigroup. The operator A is associated with a particular scalar nonatomic neutral equation.     

Global existence for second order functional semilinear equations

In this paper we study the global existence of solutions for initial value problems for functional semilinear equations, where the linear operator in the differential equation is the infinitesimal generator of a strongly cosine family in a Banach spaceX. Using the Leray-Schauder Alternative, we derive conditions under which a solution exists globally.     

Über Die Konvergenz Operatorwertiger Cosinusfunktionen mit Gestörtem Infinitesimalen Erzeuger

On convergence of operator cosine functions with perturbed infinitesimal generator. The question under what kind of perturbations a closed linear operatorA remains of the class of infinitesimal generators of operator cosine functions seems to be a rather difficult one and is unsolved in general. In this note we give bounds for the perturbation of operator cosine functions caused byA-bounded perturbationsT ofA under the assumption thatT + A is also a generator.

     

The stochastic fluid–fluid model: A stochastic fluid model driven by an uncountable-state process,which is a stochastic fluid model itself

We introduce the Stochastic Fluid–Fluid Model, which offers powerful modeling ability for a wide range of real-life systems of significance. We first derive the infinitesimal generator, with respect to time, of the driving stochastic fluid model. We then use this to derive the infinitesimal generator of a particular Laplace–Stieltjes transform of the model, which is the foundation of our analysis. We develop expressions for the Laplace–Stieltjes transforms of various performance measures for the transient and limiting analysis of the model. This work is the first direct analysis of a stochastic fluid model that is Markovian on a continuous state space.     

Almost Automorphic Functions in Frechet Spaces and Applications to Differential Equations

In this paper we first develop a theory of almost automorphic functions with values in Frechet spaces. Then, we consider the semilinear differential equation x'(t) = A x(t) + f(t, x(t)), t ∈ ℝ in a Frechet space X, where A is the infinitesimal generator of a C₀-semigroup satisfying some conditions of exponential stability. Under suitable conditions on f, we prove the existence and uniqueness of an almost automorphic mild solution to the equation.     

A second-order fluid queue with subordinator input and Markov-modulated linear output

We consider an infinite capacity second-order fluid queue with subordinator input and Markovmodulated linear release rate. The fluid queue level is described by a generalized Langevin stochastic differential equation （SDE）. Applying infinitesimal generator, we obtain the stationary distribution that satisfies an integro-differential equation. We derive the solution of the SDE and study the transient level＇s convergence in distribution. When the coefficients of the SDE are constants, we deduce the system transient property.     

判定常微分方程组具有一维李对称群的新方法

给出了判定常微分方程组接受一维李对称群的一种新方法，利用该方法证明了无穷小生成元的一个性质，所给方法比传统方法形式简单。     

Stability and asymptotic behavior of solutions for some linear partial functional differential equations in critical cases

In this work, we study the stability of the solution semigroup for some linear partial functional differential equations with infinite delay in a Banach space when the exponential stability fails. We use the so-called characteristic equation to compute the order of each pole of the resolvent operator associated with the infinitesimal generator of the solution semigroup. This result allows us to give sufficient conditions for having stability of the solution semigroup.