GLOBAL BLOW-UP FOR A LOCALIZED DEGENERATE AND SINGULAR PARABOLIC EQUATION WITH WEIGHTED NONLOCAL BOUNDARY CONDITIONS

This paper deals with the blow-up properties of positive solutions to a localized degenerate and singular parabolic equation with weighted nonlocal boundary condi- tions. Under appropriate hypotheses, the global existence and finite time blow-up of positive solutions are obtained. Furthermore, the global blow-up behavior and the uniform blow-up profile of blow-up solutions are also described. We find that the blow-up set is the whole domain {0, a}, including the boundaries, and this differs from parabolic equations with local sources case or with homogeneous Dirichlet boundary conditions case.     

Source Type Solutions of a Fourth Order Degenerate Parabolic Equation

In this paper, we study a generalized thin film equation which is relevant to capillary driven flows of thin films of power-law fluids. We prove that the generalized thin film equation in dimension d ≥ 2 has a unique C^1 source type radial self-similar nonnegative solution if 0 〈 n 〈 2p - 1 and has no solution of this type if n ≥ 2p - 1.     

Asymptotically Self-Similar Global Solutions for a Higher-Order Semilinear Parabolic System

In this paper, we study the higher-order semilinear parabolic system{ut＋（-△）^mu=a｜v｜^p-1v,（t,x）∈R^1＋×R^N,vt＋（-△）^mv=b｜u｜^q-1u,（t,x）∈R^1＋×R^N,u（0,x）=φ（x）,v（0,x）=ψ（x）,x∈R^N, where m, p,q 〉 1, a,b ∈R. We prove that the global existence of mild solutions for small initial data with respect to certain norms. Some of these solutions are proved to be asymptotically self-similar.     

A CAHN-HILLIARD TYPE EQUATION WITH GRADIENT DEPENDENT POTENTIAL

We investigate a Cahn-Hilliard type equation with gradient dependent potential. After establishing the existence and uniqueness, we pay our attention mainly to the regularity of weak solutions by means of the energy estimates and the theory of Campanato Spaces.     

STARLIKENESS AND SUBORDINATION PROPERTIES OF A LINEAR OPERATOR

In this paper, we introduce a new class of p-valent analytic functions defined by using a linear operator Lαk. For functions in this class Hαk(p, λ; h) we estimate the coefficients.Furthermore, some subordination properties related to the operator Lαkare also derived.     

INSTABILITY TO DIFFERENTIAL EQUATIONS OF FIFTH AND SIXTH ORDER WITH VARIABLE DEVIATING ARGUMENTS

In this paper, we discuss the instability of the zero solutions to certain nonlinear differential equations of fifth and sixth order with multiple retarded arguments. By the Lyapunov＇s direct method, sufficient conditions for instability of the zero solutions are obtained.     

A Nonlinear Diffusion System with Coupled Nonlinear Boundary Flux

This paper studies a nonlinear diffusion system with coupled nonlinear boundary flux and two kinds of inner sources （positive for the first and negative for the second）, where the four nonlinear mechanisms are described by eight nonlinear parameters. The critical exponent of the system is determined by a complete classification of the eight nonlinear parameters, which is represented via the characteristic algebraic system introduced to the problem.     

NUMERICAL LOCALIZATION OF ELECTROMAGNETIC IMPERFECTIONS FROM A PERTURBATION FORMULA IN THREE DIMENSIONS

This work deals with the numerical localization of small electromagnetic inhomogeneities. The underlying inverse problem considers, in a three-dimensional bounded domain, the time-harmonic Maxwell equations formulated in electric field. Typically, the domain contains a finite number of unknown inhomogeneities of small volume and the inverse problem attempts to localize these inhomogeneities from a finite number of boundary measurements. Our localization approach is based on a recent framework that uses an asymptotic expansion for the perturbations in the tangential boundary trace of the curl of the electric field. We present three numerical localization procedures resulting from the combination of this asymptotic expansion with each of the following inversion algorithms： the Current Projection method, the MUltiple Signal Classification （MUSIC） algorithm, and an Inverse Fourier method. We perform a numerical study of the asymptotic expansion and compare the numerical results obtained from the three localization procedures in different settings.     

THE CAUCHY PROBLEM OF THE HARTREE EQUATION

In this paper, we systematically study the wellposedness, illposedness of the Hartree equation, and obtain the sharp local wellposedness, the global existence in Hs, s≥1 and the small scattering result in Hs for 2 〈γ〈 n and s ≥ 2/γ - 1. In addition, we study the nonexistence of nontrivial asymptotically free solutions of the Hartree equation.     

The complexity and randomness of linear multi-secret sharing schemes with non-threshold structures

In a linear multi-secret sharing scheme with non-threshold structures, several secret values are shared among n participants, and every secret value has a specified access structure. The efficiency of a multi- secret sharing scheme is measured by means of the complexity a and the randomness . Informally, the com- plexity a is the ratio between the maximum of information received by each participant and the minimum of information corresponding to every key. The randomness is the ratio between the amount of information distributed to the set of users U = {1, …, n} and the minimum of information corresponding to every key. In this paper, we discuss a and of any linear multi-secret sharing schemes realized by linear codes with non-threshold structures, and provide two algorithms to make a and to be the minimum, respectively. That is, they are optimal.     

OSCILLATION CRITERIA FOR STRONGLY SUPERLINEAR AND STRONGLY SUBLINEAR HIGHER ORDER DYNAMIC EQUATIONS ON TIME SCALES

We establish some new criteria for the oscillation of even order nonlinear dynamic equation. We study the case of strongly super-linear and the case of strongly sub-linear subject to various conditions.     

A MONOTONE DOMAIN DECOMPOSITION ALGORITHM FOR SOLVING WEIGHTED AVERAGE APPROXIMATIONS TO NONLINEAR SINGULARLY PERTURBED PARABOLIC PROBLEMS

This paper presents and analyzes a monotone domain decomposition algorithm for solving nonlinear singularly perturbed reaction-diffusion problems of parabolic type. To solve the nonlinear weighted average finite difference scheme for the partial differential equation, we construct a monotone domain decomposition algorithm based on a Schwarz alternating method and a box-domain decomposition. This algorithm needs only to solve linear discrete systems at each iterative step and converges monotonically to the exact solution of the nonlinear discrete problem. domain decomposition algorithm is estimated The rate of convergence of the monotone Numerical experiments are presented.     

BASISITY PROBLEM AND WEIGHTED SHIFT OPERATORS

We investigate a basisity problem in the space ■p A D and in its invariant subspaces. Namely, let W denote a unilateral weighted shift operator acting in the space ■p A D,1 ≤ p ∞, by W zn= λnzn+1, n ≥ 0, with respect to the standard basis zn n≥0. Applying the so-called "discrete Duhamel product" technique, it is proven that for any integer k ≥ 1the sequence wi+nk-1 W | Ei knf n≥0is a basic sequence in Ei := span zi+n: n ≥ 0 equivalent to the basis zi+n n≥0if and only if f i = 0. We also investigate a Banach algebra structure for the subspaces Ei, i ≥ 0.     

On Global Smooth Solution of A Semi-Linear System of Wave Equations in IR^3

In this paper we consider the Cauchy problem for a semi-linear system of wave equations with Hamilton structure. We prove the existence of global smooth solution of the system for subcritical case by using conservation of energy and Strichartz＇s estimate. On the basis of Morawetz-Pohozev identity, we obtain the same result for the critical case.     

On the Cauchy Problem of the Ginzburg-Landau Equations for Atomic Fermi Gases Near the BCS-BEC Crossover

In this paper we investigate time-dependent Ginzburg-Landau equations come from the superfluid atomic Fermi-gases near the Feshbach resonance from the Fermion-Boson model. We obtain the global the equations in various spatial dimensions. existence and uniqueness of solution to     

NON-CONFLICTING ORDERING CONES AND VECTOR OPTIMIZATION IN INDUCTIVE LIMITS

Let(E, ξ) = ind(En, ξn) be an inductive limit of a sequence(En, ξn)n∈N of locally convex spaces and let every step(En, ξn) be endowed with a partial order by a pointed convex(solid) cone Sn. In the framework of inductive limits of partially ordered locally convex spaces,the notions of lastingly efficient points, lastingly weakly efficient points and lastingly globally properly efficient points are introduced. For several ordering cones, the notion of non-conflict is introduced. Under the requirement that the sequence(Sn)n∈N of ordering cones is nonconflicting, an existence theorem on lastingly weakly efficient points is presented. From this,an existence theorem on lastingly globally properly efficient points is deduced.     

SOLUTIONS TO DISCRETE MULTIPARAMETER PERIODIC BOUNDARY VALUE PROBLEMS INVOLVING THE p-LAPLACIAN VIA CRITICAL POINT THEORY

In this paper, we consider the existence of three nontrivial solutions for a discrete non-linear multiparameter periodic problem involving the p-Laplacian. By using the similar method for the Dirichlet boundary value problems in [G. Bonanno and P. Candito, Appl.Anal., 88(4)(2009), pp. 605-616], we construct two new strong maximum principles and obtain that the boundary value problem has three positive solutions for λ and μ in some suitable intervals. The approaches we use are the critical point theory.     

An Image Denoising-Deblurring Adaptive Variational Problem in BV Space

In this paper, we establish the existence and uniqueness of a BV solution to an initial boundary value problem for a nonlinear integro-differential equation, which is related to a denoising and deblurring variational model in image restoration. Several experiments relevant to the restoration model are performed and numerical results are discussed.     

BOUNDARY LAYER AND VANISHING DIFFUSION LIMIT FOR NONLINEAR EVOLUTION EQUATIONS

In this paper, we consider an initial-boundary value problem for some nonlinear evolution equations with damping and diffusion. The main purpose is to investigate the boundary layer effect and the convergence rates as the diffusion parameter α goes to zero.     

Musielak–Orlicz BMO-type Spaces Associated with Generalized Approximations to the Identity

Let X be a space of homogenous type and ψ: X × [0,∞) → [0,∞) be a growth function such that ψ(·,t) is a Muckenhoupt weight uniformly in t and ψ(x,·) an Orlicz function of uniformly upper type 1 and lower type p ∈(0,1].In this article,the authors introduce a new Musielak–Orlicz BMO-type space BMOψA(X) associated with the generalized approximation to the identity,give out its basic properties and establish its two equivalent characterizations,respectively,in terms of the spaces BMOψA,max(X) and BMOψA(X).Moreover,two variants of the John–Nirenberg inequality on BMOψA(X) are obtained.As an application,the authors further prove that the space BMOψΔ1/2(Rn),associated with the Poisson semigroup of the Laplace operator Δ on Rn,coincides with the space BMOψ(Rn) introduced by Ky.