Lp Microlocal Properties for Multi-Quasi-Elliptic Pseudodifferential Operators

2010 Mathematics Subject Classification: Primary 35S05; Secondary 35A17.

On Modified Method of Simplest Equation for Obtaining Exact Solutions of Nonlinear PDEs: Case of Elliptic Simplest Equation

2010 Mathematics Subject Classification: 74J30, 34L30.

Hypoellipticity of Anisotropic Partial Differential Equations

2002 Mathematics Subject Classification: 35S05

Sub- and Super-solutions of a Nonlinear PDE, and Application to a Semilinear SPDE

2010 Mathematics Subject Classification: 35R60, 60H15, 74H35.

Numerical solution of the Dirichlet initial boundary value problem for the heat equation in exterior 3-dimensional domains using integral equations

A numerical method for the Dirichlet initial boundary value problem for the heat equation in the exterior and unbounded region of a smooth closed simply connected 3-dimensional domain is proposed and investigated. This method is based on a combination of a Laguerre transformation with respect to the time variable and an integral equation approach in the spatial variables. Using the Laguerre transformation in time reduces the parabolic problem to a sequence of stationary elliptic problems which are solved by a boundary layer approach giving a sequence of boundary integral equations of the first kind to solve. Under the assumption that the boundary surface of the solution domain has a one-to-one mapping onto the unit sphere, these integral equations are transformed and rewritten over this sphere. The numerical discretisation and solution are obtained by a discrete projection method involving spherical harmonic functions. Numerical results are included.

Quasilinear elliptic systems with measure data

We study the existence of solutions of quasilinear elliptic systems involving $N$ equations and a measure on the right hand side, with the form $$\left\{\begin{array}{ll} -\sum_{i=1}^n \frac{\partial}{\partial x_i}\left(\sum\limits_{\beta=1}^{N}\sum\limits_{j=1}^{n}% a_{i,j}^{\alpha,\beta}\left( x,u\right)\frac{\partial}{\partial x_j}u^\beta\right)=\mu^\alpha& \mbox{ in }\Omega ,\\ u=0 & \mbox{ on }\partial\Omega, \end{array}\right.$$ where $\alpha\in\{1,\dots,N\}$ is the equation index, $\Omega$ is an open bounded subset of $\mathbb{R}^{n}$, $u:\Omega\rightarrow\mathbb{R}^{N}$ and $\mu$ is a finite Randon measure on $\mathbb{R}^{n}$ with values into $\mathbb{R}^{N}$. Existence of a solution is proved for two different sets of assumptions on $A$. Examples are provided that satisfy our conditions, but do not satisfy conditions required on previous works on this matter.

Symmetric Interior Penalty DG Methods for the Compressible Navier-Stokes Equations I: Method Formulation

In this article we consider the development of discontinuous Galerkin finite element methods for the numerical approximation of the compressible Navier-Stokes equations. For the discretization of the leading order terms, we propose employing the generalization of the symmetric version of the interior penalty method, originally developed for the numerical approximation of linear self-adjoint second-order elliptic partial differential equations. In order to solve the resulting system of nonlinear equations, we exploit a (damped) Newton-GMRES algorithm. Numerical experiments demonstrating the practical performance of the proposed discontinuous Galerkin method with higher-order polynomials are presented.

A Posteriori Error Analysis of hp-Version Discontinuous Galerkin Finite Element Methods for Second-Order Quasilinear Elliptic Problems

We develop the a-posteriori error analysis of hp-version interior-penalty discontinuous Galerkin finite element methods for a class of second-order quasilinear elliptic partial differential equations. Computable upper and lower bounds on the error are derived in terms of a natural (mesh-dependent) energy norm. The bounds are explicit in the local mesh size and the local degree of the approximating polynomial. The performance of the proposed estimators within an automatic hp-adaptive refinement procedure is studied through numerical experiments.

An Extension of the Invariance Principle for a Class of Differential Equations with Finite Delay

An extension of the uniform invariance principle for ordinary differential equations with finite delay is developed. The uniform invariance principle allows the derivative of the auxiliary scalar function V to be positive in some bounded sets of the state space while the classical invariance principle assumes that. V <= 0. As a consequence, the uniform invariance principle can deal with a larger class of problems. The main difficulty to prove an invariance principle for functional differential equations is the fact that flows are defined on an infinite dimensional space and, in such spaces, bounded solutions may not be precompact. This difficulty is overcome by imposing the vector field taking bounded sets into bounded sets.

EXISTENCE RESULTS FOR NEUTRAL INTEGRO-DIFFERENTIAL EQUATIONS WITH UNBOUNDED DELAY

In this paper we discuss the existence of mild, strict and classical solutions for a class of abstract integro-differential equations in Banach spaces. Some applications to ordinary and partial integro-differential equations are considered.

GLOBAL SOLUTIONS FOR ABSTRACT FUNCTIONAL DIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS

In this paper we study the existence of global solutions for a class of abstract functional differential equation with nonlocal conditions. An application is considered.

Weighted S-Asymptotically omega-Periodic Solutions of a Class of Fractional Differential Equations

We study the existence of weighted S-asymptotically omega-periodic mild solutions for a class of abstract fractional differential equations of the form u' = partial derivative (alpha vertical bar 1)Au + f(t, u), 1 < alpha < 2, where A is a linear sectorial operator of negative type.

EXISTENCE RESULTS FOR ABSTRACT NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS

In this paper we discuss the existence of solutions for a class of abstract partial neutral functional differential equations.

Centrality dependence of charged hadron and strange hadron elliptic flow from root s(NN)=200 GeVAu+Au collisions

We present STAR results on the elliptic flow upsilon(2) Of charged hadrons, strange and multistrange particles from,root s(NN) = 200 GeV Au+Au collisions at the BNL Relativistic Heavy Ion Collider (RHIC). The detailed study of the centrality dependence of upsilon(2) over a broad transverse momentum range is presented. Comparisons of different analysis methods are made in order to estimate systematic uncertainties. To discuss the nonflow effect, we have performed the first analysis Of upsilon(2) with the Lee-Yang zero method for K(S)(0) and A. In the relatively low PT region, P(T) <= 2 GeV/c, a scaling with m(T) - m is observed for identified hadrons in each centrality bin studied. However, we do not observe nu 2(p(T))) scaled by the participant eccentricity to be independent of centrality. At higher PT, 2 1 <= PT <= 6 GeV/c, V2 scales with quark number for all hadrons studied. For the multistrange hadron Omega, which does not suffer appreciable hadronic interactions, the values of upsilon(2) are consistent with both m(T) - m scaling at low p(T) and number-of-quark scaling at intermediate p(T). As a function ofcollision centrality, an increase of p(T)-integrated upsilon(2) scaled by the participant eccentricity has been observed, indicating a stronger collective flow in more central Au+Au collisions.

Elliptic and Hexadecapole Flow of Charged Hadrons in Au plus Au Collisions at root s(NN)=200 GeV

Differential measurements of the elliptic (upsilon(2)) and hexadecapole (upsilon(4)) Fourier flow coefficients are reported for charged hadrons as a function of transverse momentum (p(T)) and collision centrality or number of participant nucleons (N(part)) for Au + Au collisions at root s(NN) = 200 GeV/ The upsilon(2,4) measurements at pseudorapidity vertical bar eta vertical bar <= 0.35, obtained with four separate reaction-plane detectors positioned in the range 1.0 < vertical bar eta vertical bar < 3.9, show good agreement, indicating the absence of significant Delta eta-dependent nonflow correlations. Sizable values for upsilon(4)(p(T)) are observed with a ratio upsilon(4)(p(T), N(part))/upsilon(2)(2)(p(T), N(part)) approximate to 0.8 for 50 less than or similar to N(part) less than or similar to 200, which is compatible with the combined effects of a finite viscosity and initial eccentricity fluctuations. For N(part) greater than or similar to 200 this ratio increases up to 1.7 in the most central collisions.