EXISTENCE OF ENTROPY SOLUTIONS TO TWO-DIMENSIONAL STEADY EXOTHERMICALLY REACTING EULER EQUATIONS

We are concerned with the global existence of entropy solutions of the twodimensional steady Euler equations for an ideal gas, which undergoes a one-step exothermic chemical reaction under the Arrhenius-type kinetics. The reaction rate function φ(T) is assumed to have a positive lower bound. We first consider the Cauchy problem(the initial value problem), that is, seek a supersonic downstream reacting flow when the incoming flow is supersonic, and establish the global existence of entropy solutions when the total variation of the initial data is suffciently small. Then we analyze the problem of steady supersonic, exothermically reacting Euler flow past a Lipschitz wedge, generating an additional detonation wave attached to the wedge vertex, which can be then formulated as an initial-boundary value problem. We establish the global existence of entropy solutions containing the additional detonation wave(weak or strong, determined by the wedge angle at the wedge vertex) when the total variation of both the slope of the wedge boundary and the incoming flow is suitably small. The downstream asymptotic behavior of the global solutions is also obtained.     

WELL-POSEDNESS OF A COMPRESSIBLE GAS-LIQUID MODEL FOR DEEPWATER OIL WELL OPERATIONS

The main purpose of this paper is two-fold:(i) to generalize an existence result for a compressible gas-liquid model with a friction term recently published by Friis and Evje [SIAM J. Appl. Math., 71(2011), pp. 2014–2047];(ii) to derive a uniqueness result for the same model. A main ingredient in the existence part is the observation that we can consider weaker assumptions on the initial liquid and gas mass, and still obtain an existence result. Compared to the above mentioned work, we rely on a more refined application of the estimates provided by the basic energy estimate. Concerning the uniqueness result, we borrow ideas from Fang and Zhang [Nonlinear Anal. TMA, 58(2004), pp. 719–731] and derive a stability result under appropriate constraints on parameters that determine rate of decay toward zero at the boundary for gas and liquid masses, and growth rate of masses associated with the friction term and viscous coefficient.     

ON THE ASYMPTOTIC BEHAVIOR OF HOLOMORPHIC ISOMETRIES OF THE POINCARE 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.     

THE NAVIER-STOKES EQUATIONS WITH THE KINEMATIC AND VORTICITY BOUNDARY CONDITIONS ON NON-FLAT BOUNDARIES

We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a general domain in R^n with compact and smooth boundary, subject to the kinematic and vorticity boundary conditions on the non-flat boundary. We observe that, under the nonhomogeneous boundary conditions, the pressure p can be still recovered by solving the Neumann problem for the Poisson equation. Then we establish the well-posedness of the unsteady Stokes equations and employ the solution to reduce our initial-boundary value problem into an initial-boundary value problem with absolute boundary conditions. Based on this, we first establish the well-posedness for an appropriate local linearized problem with the absolute boundary conditions and the initial condition （without the incompressibility condition）, which establishes a velocity mapping. Then we develop apriori estimates for the velocity mapping, especially involving the Sobolev norm for the time-derivative of the mapping to deal with the complicated boundary conditions, which leads to the existence of the fixed point of the mapping and the existence of solutions to our initial-boundary value problem. Finally, we establish that, when the viscosity coefficient tends zero, the strong solutions of the initial-boundary value problem in R^n（n ≥ 3） with nonhomogeneous vorticity boundary condition converge in L^2 to the corresponding Euler equations satisfying the kinematic condition.     

MULTIPLICATION OPERATORS ON INVARIANT SUBSPACES OF FUNCTION SPACES

Let M? be the operator of multiplication by?on a Hilbert space of functions analytic on the open unit disk. For an invariant subspace F for the multiplication operator Mz, we derive some spectral prope...     

NORMALLY DISTRIBUTED PROBABILITY MEASURE ON THE METRIC SPACE OF NORMS

In this paper we propose a method to construct probability measures on the space of convex bodies. For this purpose, first, we introduce the notion of thinness of a body. Then we show the existence of ...     

SUBORDINATION PROPERTIES OF MULTIVALENT FUNCTIONS INVOLVING AN EXTENDED FRACTIONAL DIFFERINTEGRAL OPERATOR

The object of this article is to investigate inclusion, radius, and other various properties of subclasses of multivalent analytic functions, which are defined by using an extended version of the Owa-Srivastava fractional differintegral operator Ω(λ,p).     

ON THE EXISTENCE OF SINGULAR DIRECTIONS OF HOLOMORPHIC MAPS FROM THE UNIT DISK INTO Pn（C）

This article proves the existence of Julia directions of value distribution of holomorphic mapping f from the unit disk into the n-dimensional complex projective space P n(C) under the assumption lim sup r→1-T(r,f)/log 1/1-r=+∞ for hypersurfaces in general position.A heuristic principle concerning the existence of Julia directions of holomorphic mappings from the unit disk into P n(C) is given also.     

STRONG COMPACTNESS OF APPROXIMATE SOLUTIONS TO DEGENERATE ELLIPTIC-HYPERBOLIC EQUATIONS WITH DISCONTINUOUS FLUX FUNCTION

Under a non-degeneracy condition on the nonlinearities we show that sequences of approximate entropy solutions of mixed elliptic-hyperbolic equations are strongly precompact in the general case of a Caratheodory flux vector. The proofs are based on deriving localization principles for H-measures associated to sequences of measurevalued functions. This main result implies existence of solutions to degenerate parabolic convection-diffusion equations with discontinuous flux. Moreover, it provides a framework in which one can prove convergence of various types of approximate solutions, such as those generated by the vanishing viscosity method and numerical schemes.     

GENERALIZED DERIVATIONS ON PARABOLIC SUBALGEBRAS OF GENERAL LINEAR LIE ALGEBRAS

Let P be a parabolic subalgebra of a general linear Lie algebra gl(n, F) over a field F, where n ≥ 3, F contains at least n different elements, and char(F) = 2. In this article, we prove that generalized derivations, quasiderivations, and product zero derivations of P coincide, and any generalized derivation of P is a sum of an inner derivation, a central quasiderivation, and a scalar multiplication map of P. We also show that any commuting automorphism of P is a central automorphism, and any commuting derivation of P is a central derivation.     

CONSTRUCTION OF OPTIMAL BLOCKING SCHEMES FOR ROBUST PARAMETER DESIGNS

Robust parameter design (RPD) is an important issue in experimental designs. If all experimental runs cannot be performed under homogeneous conditions, blocking the units is effective. In this paper, w...     

ON INTERSECTIONS OF INDEPENDENT NONDEGENERATE DIFFUSION PROCESSES

Let X(1)= {X(1)(s), s ∈ R+ } and X(2)= {X(2)(t), t ∈ R+ } be two independent nondegenerate diusion processes with values in Rd. The existence and fractal dimension of intersections of the sample paths of X(1)and X(2)are studied. More generally, let E1, E2 ■(0, ∞) and F  Rd be Borel sets. A necessary condition and a suffcient condition for P{X(1)(E1) ∩ X(2)(E2) ∩ F = φ} 0 are proved in terms of the Bessel-Riesz type capacity and Hausdor measure of E1 ×E2 ×F in the metric space(R+ ×R+ ×Rd, ρ), where ρ is an unsymmetric metric defined in R+ × R+ × Rd. Under reasonable conditions, results resembling those of Browian motion are obtained.     

POSITIVE SOLUTIONS FOR PARAMETRIC EQUIDIFFUSIVE p-LAPLACIAN EQUATIONS

We consider a parametric Dirichlet problem driven by the p-Laplacian with a Carath′eodory reaction of equidiffusive type. Our hypotheses incorporate as a special case the equidiffusive p-logistic equation. We show that if λ1 0 is the principal eigenvalue of the Dirichlet negative p-Laplacian and λ λ1(λ being the parameter), the problem has a unique positive solution, while for λ∈(0,λ1], the problem has no positive solution.     

SPHERICAL SYMMETRIC SOLUTIONS FOR THE MOTION OF RELATIVISTIC MEMBRANES AND NULL MEMBRANES IN THE REISSNER-NORDSTROM SPACE-TIME

In this article, we concern the motion of relativistic membranes and null mem- branes in the Reissner-Nordstrom space-time. The equation of relativistic membranes moving in the Reissner-Nordstrom space-time is derived and some properties are discussed. Spherical symmetric solutions for the motion are illustrated and some interesting physical phenomena are discovered. The equations of the null membranes are derived and the exact solutions are also given. Spherical symmetric solutions for null membranes are just the two horizons of Reissner-NordstrSm space-time.     

A REACTIVE DYNAMIC CONTINUUM USER EQUILIBRIUM MODEL FOR BI-DIRECTIONAL PEDESTRIAN FLOWS

In this paper, a reactive dynamic user equilibrium model is extended to simulate two groups of pedestrians traveling on crossing paths in a continuous walking facility. Each group makes path choices to minimize the travel cost to its destination in a reactive manner based on instantaneous information. The model consists of a conservation law equation coupled with an Eikonal-type equation for each group. The velocity-density relationship of pedestrian movement is obtained via an experimental method. The model is solved using a finite volume method for the conservation law equation and a fast-marching method for the Eikonal-type equation on unstructured grids. The numerical results verify the rationality of the model and the validity of the numerical method. Based on this continuum model, a number of results, e.g., the formation of strips or moving clusters composed of pedestrians walking to the same destination, are also observed.     

SYMMETRY OF TRANSLATING SOLUTIONS TO MEAN CURVATURE FLOWS

First, we review the authors’ recent results on translating solutions to mean curvature flows in Euclidean space as well as in Minkowski space, emphasizing on the asymptotic expansion of rotationally symmetric solutions. Then we study the sufficient condition for which the translating solution is rotationally symmetric. We will use a moving plane method to show that this condition is optimal for the symmetry of solutions to fully nonlinear elliptic equations without ground state condition.     

ON THE SINGULARITY OF LEAST SQUARES ESTIMATOR FOR MEAN-REVERTING α-STABLE MOTIONS

We study the problem of parameter estimation for mean-reverting α-stable motion, dXt = （a0 - θ0Xt）dt ＋ dZt, observed at discrete time instants. A least squares estimator is obtained and its asymptotics is discussed in the singular case （a0, θ0） = （0, 0）. If a0 = 0, then the mean-reverting α-stable motion becomes Ornstein-Uhlenbeck process and is studied in [7] in the ergodic case θ0 〉 0. For the Ornstein-Uhlenbeck process, asymptotics of the least squares estimators for the singular case （θ0 = 0） and for ergodic case （θ0 〉 0） are completely different.     

THE JUMPING PHENOMENON OF THE DIMENSIONS OF COHOMOLOGY GROUPS OF TANGENT SHEAF

Let X be a compact complex manifold.Consider a small deformation π :X→B of X,the dimensions of the cohomology groups of tangent sheaf H q(X_t,T_X_t) may vary under this deformation.This article studies such phenomena by studying the obstructions to deform a class in H q(X,T X) with parameter t and gets a formula for the obstructions.     

EXISTENCE OF POSITIVE SOLUTIONS TO SEMILINEAR ELLIPTIC SYSTEMS IN IRN WITH ZERO MASS

In this paper, we prove the existence of at least one positive solution pairto the following semilinear elliptic systemby using a linking theorem, where K（x）is a positive function in L^s（R^N） for some s 〉 1and the nonnegative functions f, g ∈ C（R, R） are of quasicritical growth, superlinear atinfinity. We do not assume that f or g satisfies the Ambrosetti-Rabinowitz condition as usual. Our main result can be viewed as a partial extension of a recent result of Alves, Souto and Montenegro in [1] concerning the existence of a positive solution to the following semilinear elliptic problemand a recent result of Li and Wang in [22] concerning the existence of nontrivial solutions to a semilinear elliptic system of Hamiltonian type in R^N.     

WEIGHTED ESTIMATES FOR COMMUTATORS OF MULTILINEAR CALDERON-ZYGMUND OPERATORS WITH NON-DOUBLING MEASURES

Let μ be a nonnegative Radon measure on Rd, which only satisfies the polynomial growth condition. Under this assumption, the authors obtain some weighted weaktype estimates for the commutators generated by the multilinear CalderSn-Zygmund op- erators and RBMO（μ） functions.