MINIMIZERS OF L^(2)-SUBCRITICAL VARIATIONAL PROBLEMS WITH SPATIALLY DECAYING NONLINEARITIES IN BOUNDED DOMAINS

This paper is concerned with the minimizers of L^(2)-subcritical constraint variar tional problems with spatially decaying nonlinearities in a bounded domain Ω of R~N(N≥1).We prove that the problem admits minimizers for any M> 0.Moreover,the limiting behavior of minimizers as M→∞ is also analyzed rigorously.

INCOMPRESSIBLE LIMIT OF THE NON-ISENTROPIC MAGNETOHYDRODYNAMIC EQUATIONS IN BOUNDED DOMAINS

The incompressible limit of the non-isentropic magnetohydrodynamic equations with zero thermal coefficient, in a two dimensional bounded domain with the Dirichlet condi- tion for velocity and perfectly conducting boundary condition for magnetic field, is rigorously justified.

Multilinear Fractional Integral Operators on Morrey Spaces with Variable Exponent on Bounded Domain

We prove the boundedness of multilinear fractional integral operators onproducts of the variable exponent Morrey spaces on bounded domain.

Pullback attractor of 2D non-autonomous g-Navier-Stokes equations on some bounded domains

The existence of the pullback attractor for the 2D non-autonomous g-Navier- Stokes equations on some bounded domains is investigated under the general assumptions of pullback asymptotic compactness. A new method to prove the existence of the pullback attractor for the 2D g-Navier-Stokes eauations is given.

The Integral Representations and Their Applications on the Analytic Varieties of Bounded Domains in Stein Manifolds

In this paper,we first obtain a unified integral representation on the analytic varieties of the general bounded domain in Stein manifolds(the two types bounded domains in[3]are regarded as its special cases).Secondly we get the integral formulas of the solution of∂-equation.And we use a new and unique method to give a uniform estimate of the solution of∂-equation,which is different from Henkin's method.

Global Existence of Solutions for Baer-Nunziato Two-Phase Flow Model in a Bounded Domain

In this paper, we study the global existence and uniqueness of strong solutions for the Baer-Nunziato two-phase flow model in a bounded domain with a no-slip boundary. The global existence and uniqueness of strong solutions are obtained when the initial value is near the equilibrium state in H2 (Ω). Furthermore, the exponential convergence rates of the pressure and velocity are also proved by delicate energy methods.

On the inviscid limit of the compressible Navier-Stokes equations near Onsager's regularity in bounded domains

The viscous dissipation limit of weak solutions is considered for the Navier-Stokes equations of compressible isentropic flows confined in a bounded domain.We establish a Kato-type criterion for the validity of the inviscid limit for the weak solutions of the Navier-Stokes equations in a function space with the regularity index close to Onsager’s critical threshold.In particular,we prove that under such a regularity assumption,if the viscous energy dissipation rate vanishes in a boundary layer of thickness in the order of the viscosity,then the weak solutions of the Navier-Stokes equations converge to a weak admissible solution of the Euler equations.Our approach is based on the commutator estimates and a subtle foliation technique near the boundary of the domain.

The low Mach number limit of non-isentropic magnetohydrodynamic equations with large temperature variations in bounded domains

This paper verifies the low Mach number limit of the non-isentropic compressible magnetohydrodynamic(MHD)equations with or without the magnetic diffusion in a three-dimensional bounded domain when the temperature variation is large but finite.The uniform estimates of strong solutions are established in a short time interval independent of the Mach number,provided that the slip boundary condition for the velocity and the Neumann boundary condition for the temperature are imposed and the initial data is well-prepared.

Regularity Criteria of the Magnetohydrodynamic Equations in a Bounded Domain

Regularity criteria in terms of bounds for the pressure are derived for the 3D MHD equations in a bounded domain with slip boundary conditions.A list of three regularity criteria is shown.

Eigenvalues of the Negative Laplacian for Simply Connected Bounded Domains

This paper is devoted to asymptotic formulae for functions related with the spectrum of the negative Laplacian in two and three dimensional bounded simply connected domains with impedance boundary conditions,where the impedances are assumed to be discontinuous functions. Moreover,asymptotic expressions for the difference of eigenvalues related to the impedance problems with different impedances are derived.Further results may be obtained.

Global dynamics of a nonlocal population model with age structure in a bounded domain:A non-monotone case

We study the global dynamics of a nonlocal population model with age structure in a bounded domain. We mainly concern with the case where the birth rate decreases as the mature population size become large. The analysis is rather subtle and it is inadequate to apply the powerful theory of monotone dynamical systems. By using the method of super-sub solutions, combined with the careful analysis of the kernel function in the nonlocal term, we prove nonexistence, existence and uniqueness of positive steady states of the model.Moreover, due to the mature individuals do not diffuse, the solution semiflow to the model is not compact. To overcome the difficulty of non-compactness in describing the global asymptotic stability of the unique positive steady state, we first establish an appropriate comparison principle. With the help of the comparison principle,we can employ the theory of dissipative systems to obtain the global asymptotic stability of the unique positive steady state. The main results are illustrated with the nonlocal Nicholson's blowflies equation and the nonlocal Mackey-Glass equation.

The Static Solution for the Layered Piezoelectric Bounded Domain with Side Face Load by the Modified SBFEM

The static response of two-dimensional horizontal layered piezoelectric bounded domain with side face load was investigated.In this paper,the modified scaled boundary finite element method(SBFEM)is provided as an effective semi analytical methodology.The method is used to solve the static problem for the layered piezoelectric bounded domain.The scaling line definition extends the SBFEM to be more suitable for analyzing the multilayered piezoelectric bounded domain.It avoids the limitations of original SBFEM in modeling the horizontal layered bounded domain.The modified SBFEM governing equation with piezoelectric medium is derived by introducing Duality variable in the Hamilton system.This derivation technology makes the progress be concise.The novel displacement and electric governing equations of the modified SBFEM is given together by the first time.The node forces can be expressed as power exponent function with radial coordinate by introducing the auxiliary variable and using the eigenvalue decomposition.The novel modified SBFEM solution of layered bounded domain with piezoelectric medium is solved.The new power expansion function of layered piezoelectric medium with side face load is proposed.This technology significantly extends the application range of modified SBFEM.The novel treatment of side face load for the layered piezoelectric bounded domain is proposed.Numerical studies are conducted to demonstrate the accuracy of proposed technique in handling with the static problem of layered bounded domain with piezoelectric medium for side face load.The influence of the side face load type and depth are discussed in detail.

THE EQUIVALENT CHARACTERIZATION OF F(p,q,s)SPACE ON BOUNDED SYMMETRIC DOMAINS OF Cn

LetΩ be a bounded symmetric domain in Cn. The purpose of this article is to define and characterize the general function space F（p, q, s） on Ω. Characterizing functions in the F（p, q, s） space is a work of considerable interest nowadays. In this article, the authors give several equivalent descriptions of the functions in the F（p, q, s） space on Ω in terms of fractional differential operators. At the same time, the authors give the relationship between F（p, q, s） space and Bloch type space on Ω too.

ON THE ASYMPTOTIC BEHAVIOR OF HOLOMORPHIC ISOMETRIES OF THE POINCAR DISK INTO BOUNDED SYMMETRIC DOMAINS

In this article we bounded symmetric domains study holomorphic isometries of the Poincare disk into Earlier we solved the problem of analytic continuation of germs of holomorphic maps between bounded domains which are isometrics up to normalizing constants with respect to the Bergman metric, showing in particular that the graph 170 of any germ of holomorphic isometry of the Poincar6 disk A into an irreducible bounded symmetric domain Ω belong to C^N in its Harish-Chandra realization must extend to an affinealgebraic subvariety V belong to C × C^N = C^N＋1, and that the irreducible component of V ∩ （△ × Ω） containing V0 is the graph of a proper holomorphic isometric embedding F ： A→ Ω. In this article we study holomorphie isometric embeddings which are asymptotically geodesic at a general boundary point b ∈ δ△. Starting with the structural equation for holomorphic isometrics arising from the Gauss equation, we obtain by covariant differentiation an identity relating certain holomorphic bisectional curvatures to the boundary behavior of the second fundamental form σ of the holomorphie isometric embedding. Using the nonpositivity of holomorphic bisectional curvatures on a bounded symmetric domain, we prove that ‖σ‖ must vanish at a general boundary point either to the order 1 or to the order 1/2, called a holomorphie isometry of the first resp. second kind. We deal with special cases of non-standard holomorphic isometric embeddings of such maps, showing that they must be asymptotically totally geodesic at a general boundary point and in fact of the first kind whenever the target domain is a Cartesian product of complex unit balls. We also study the boundary behavior of an example of holomorphic isometric embedding from the Poincare disk into a Siegel upper half-plane by an explicit determination of the boundary behavior of holomorphic sectional curvatures in the directions tangent to the embedded Poincare disk, showing that the map is indeed asymptotically totally geodesic at a general boundary point and of the first kind. For the metric computation we make use of formulas for symplectic geometry on Siegel upper half-planes.

A NEW ROPER-SUFFRIDGE EXTENSION OPERATOR ON BOUNDED COMPLETE REINHARDT DOMAINS

In this paper, we construct a new Roper-Suffridge extension operator Φn^r,β1,,βn（f）（z） = F（z） = （（rf（z1/r）/z1）^β1z1,（rf（z1/r）/z1）^β2z2,...,（rf（z1/r）/z1）^βnzn）＇,where f is a normalized locally biholomorphic function on the unit disc D, r = sup{｜z1｜ ： z =（z1, ···, zn） ∈Ω}, β1∈ [0, 1], 0 ≤βk≤β1, k = 2, ···, n, then we prove it can preserve the property of spirallikeness of type β, almost starlikeness of order α and starlikeness of orderα on bounded complete Reinhardt domain Ω, respectively.

α-CARLESON MEASURE AND BLOCH FUNCTIONS ON BOUNDED SYMMETRIC DOMAINS OF C^n

In this paper we defineα-Carleson measure in the Bergman metric on bounded symmetric domains. Some necessary and sufficient conditions about it and Bloch functions on the domains are given.

The Covering Theorems for Normalized Holomorphic Mappings on Bounded Starlike Circular Domains in C^n

In this paper, we will investigate convex domains and starlike domains which contain the image set of normalized holomorphic mappings on bounded starlike circular domains in Cn.

Function Theory of a Class of Bounded Reinhardt Domains

In this paper, we consider a class of bounded Reinhardt domains Dα（m, n1,…,nm）. The Bergman kernel function K（z,z^）, the Bergman metric matrix T（z,z^）, the Cauchy-Szegoe kernel function S（z,ζ^） are obtained. Then we prove that the formal Poisson kernel function is not a Poisson kernel function. At last, we prove that Dα is a quasiconvex domain and Dα is a stronger quasiconvex domain if and only if Dα is a hypersphere.

Weighted Bergman Spaces on Bounded Symmetric Domains

On bounded symmetric domain Ω of C^n, we investigate the properties of functions in weighted Bergman spaces A^P（Ω,dvs） for 0 〈 p ≤ ＋∞ and -1 〈 s 〈 4-∞. Based on the estimate of Bergman kernel, we obtain some characterizations of functions in A^P（Ω, dvs） in terms of a class of linear operators D^αB. Making use of these characterizations, we extend A^P（Ω,dvs） to the weighted Bergman spaces Aα^p,B（Ω,dvs） in a very natural way for 1 〈 p 〈 4-∞ and any real number s, that is, -∞ 〈 s 〈 ＋∞. This unified treatment covers some classical Bergman spaces, Besov spaces and Bloch spaces. Meanwhile, the boundedness of Bergman projection operators on Aα^P,β（Ω, dvs） and the dual of Aα^P,B（Ω, dvs） are given.

INVERSE PROBLEMS FOR A GENERAL MULTI-CONNECTED BOUNDED DRUM WITH APPLICATIONS IN PHYSICS

This paper studies the influence of a finite container on an ideal gas.The trace of the heat kernel (t) =exp, where are the eigenvalues of the negative Laplacian -in Rn(n = 2 or 3), is studied for a general multi-connected bounded drum ft which is surrounded by simply connected bounded domains Ωi with smooth boundaries Ωi(i = 1,… ,m) where the Dirichlet, Neumann and Robin boundary conditions on Ωi(i = 1,…,m) are considered. Some geometrical properties of Ω are determined. The thermodynamic quantities for an ideal gas enclosed in Ω are examined by using the asymptotic expansions of (t) for short-time t. It is shown that the ideal gas can not feel the shape of its container Ω, although it can feel some geometrical properties of it.