Analyticity and exponential stability of semigroups for the elastic systems with structural damping in Banach spaces

In this paper, we consider a second order evolution equation in a Banach space, which can model an elastic system with structural damping. New forms of the corresponding first order evolution equation are introduced, and their well-posed property is proved by means of the operator semigroup theory. We give sufficient conditions for analyticity and exponential stability of the associated semigroups.     

On the uniqueness and analyticity of solutions in micropolar thermoviscoelasticity

This paper deals with the linear theory of isotropic micropolar thermoviscoelastic materials. When the dissipation is positive definite, we present two uniqueness theorems. The first one requires the extra assumption that some coupling terms vanish; in this case, the instability of solutions is also proved. When the internal energy and the dissipation are both positive definite, we prove the well-posedness of the problem and the analyticity of the solutions. Exponential decay and impossibility of localization are corollaries of the analyticity.     

磁流体方程的时间解析半径

本文考查了二维周期边界条件下的磁流体方程 ,证明了当初值位于全局吸引子上和定常解足够接近时 ,解在t=0的时间解析半径可以任意大     

A renormalization group explanation of numerical observations of analyticity domains

A recent paper considers the dependence of the size of analyticity domains of some functions appearing in KAM theory as a function of the distance to breakdown. They tentatively conclude that the relation is linear. In this note we argue that McKay's renormalization group picture predicts a power-law dependence with an exponent close to 1 but not equal to 1.     

On the Analyticity of Underlying HKM Paths for Monotone Semidefinite Linear Complementarity Problems

An interior point method (IPM) defines a search direction at an interior point of the feasible region. These search directions form a direction field, which in turn defines a system of ordinary differential equations (ODEs). The solutions of the system of ODEs are called off-central paths, underlying paths lying in the interior of the feasible region. It is known that not all off-central paths are analytic, whether w.r.t. μ or , where μ represents the duality gap, at a solution of a given semidefinite linear complementarity problem, SDLCP (Sim and Zhao, Math. Program. 110:475–499, 2007). In Sim and Zhao (J. Optim. Theory Appl. 137:11–25, 2008), we give a necessary and sufficient condition for when an off-central path is analytic as a function of at a solution of a general SDLCP. It is then natural to ask about the analyticity of a SDLCP off-central path at a solution, as a function of μ. We investigate this in the current paper. Again, we work under the assumption that the given SDLCP satisfies strict complementarity condition.     

Analyticity of solutions of semi-linear equations with double characteristics

We prove the analyticity and Gevrey regularity of solutions of elliptic degenerate semi-linear differential equations principle part of which is a linear operator with double characteristics considered first by Gilioli and Treves. A new elementary proof for hypoellipticity in the weak sense is given.     

Analyticity of strictly static and strictly stationary,inheriting and non-inheriting Einstein–Maxwell solutions

Following the technique of Müller zum Hagen (Proc. Camb. Phil. Soc. 67: 415–421, 1970) we show that strictly static and strictly stationary solutions of the Einstein–Maxwell equations are analytic in harmonic coordinates. This holds whether or not the Maxwell field inherits the symmetry.     

Mindlin–Timoshenko systems with Kelvin–Voigt: analyticity and optimal decay rates

This paper is concerned with asymptotic stability of Mindlin–Timoshenko plates with dissipation of Kelvin–Voigt type on the equations for the rotation angles. We prove that the corresponding evolution semigroup is analytic if a viscoelastic damping is also effective over the equation for the transversal displacements. On the contrary, if the transversal displacement is undamped, we show that the semigroup is neither analytic nor exponentially stable. In addition, in the latter case, we show that the solution decays polynomially and we prove that the decay rate found is optimal.     

ANALYTIC FUNCTIONALS AND A NEW DISTRIBUTION THEORY OVER INFINITE DIMENSIONAL SPACES

§1.ＩｎｔｒｏｄｕｃｔｉｏｎａｎｄＢａｃｋｇｒｏｕｎｄ　　ＴｈｅｄｉｓｔｒｉｂｕｔｉｏｎｔｈｅｏｒｙｏｖｅｒｉｎｆｉｎｉｔｅｄｉｍｅｎｓｉｏｎａｌＧａｕｓｓｉａｎｓｐａｃｅｈａｓｂｅｅｎｄｅｖｅｌｏｐｅｄｉｎｔｗｏｄｉｒｅｃｔｉｏｎｓ:Ｇｉｖｅｎａｄｅｎｓｅｌｙｄｅｆｉｎｅｄｎｏｎ-ｎｅｇａｔｉｖｅｓｅｌｆａｄｊｏｉｎｔｏｐｅｒａｔｏｒＡｉｎｔｈｅＨｉｌｂｅｒｔｓｐａｃｅＬ2(Ｒ),ｂｙｔｈｅｗｅｌｌ-ｋｎｏｗｎｉｓｏｍｏｒｐｈｉｓｍｂｅｔｗｅｅｎ(Ｌ2),ｔｈｅＨｉｌｂｅｒｔｓｐａｃｅｏｆｓｑｕａｒｅｉ…