In this article we consider the Primitive Equations without horizontal viscosity but with a mild vertical viscosity added in the hydrostatic equation, as in [13] and [16], which are the so-called δ−Primitive Equations. We prove that the problem is well posed in the sense of Hadamard in certain types of spaces. This means that we prove the finite-in-time existence, uniqueness and continuous depe...

| The relative accuracy of several local radiation boundary conditions based on the second-order Bayliss{Turkel condition are evaluated. These boundary conditions permit the approximate solution of the scalar Helmholtz equation in an in nite domain using traditional nite element and nite di erence techniques. Unlike the standard BaylissTurkel condition, the generalizations considered here are a...

We show a superconvergence property for the Semi-Lagrangian Discontinuous Galerkin scheme of arbitrary degree in the case of constant linear advection equation with periodic boundary conditions.

We show that there is no blowup solutions, for positive viscosity constant , to the equation f xxt f xxxx +ff xxx f x f xx = 0; x 2 (0; 1); t > 0 with (i) periodic boundary condition, or (ii) Dirichlet boundary condition f = f x = 0 or (iii) Neumann boundary condition f = f xx = 0 on the boundary x = 0; 1. Furthermore we show that every solution decays to the trivial steady state as t goes to i...

Polynomials orthogonal on the unit circle with random recurrence coefficients and finite band spectrum are investigated. It is shown that the coefficients are in fact quasiperiodic. The measures associated with these quasi-periodic coefficients are exhibited and necessary and sufficient conditions relating quasi-periodicity and spectral measures of this type are given. Analogs for polynomials o...

We show how the (globally supersymmetric) model of Mirabelli and Peskin can be formulated in the boundary (“downstairs” or “interval”) picture. The necessary GibbonsHawking-like terms appear naturally when using (codimension one) superfields. This formulation is free of the δ(0) ambiguities of the orbifold (“upstairs”) picture while describing the same physics since the boundary conditions on t...

In this section, we will introduce the work of Kbabou, Hermi, and Rhonma (2007)[2]. Their main idea is to use the eigenvalues and their ratios of the Dirichlet-Laplacian for various planar shapes as their features for classifying them. Let the sequence 0 < λ 1 < λ 2 ≤ λ 3 ≤ · · · ≤ λ k ≤ · · · → ∞ be the sequence of eigenvalues of Dirichlet-Laplacian problem: −∆u = λu in a given bounded planar ...

The relativistic Boltzmann equation for a constant differential cross section and with periodic boundary conditions is considered. The speed of light appears as a parameter c>c0 for a properly large and positive c0. A local existence and uniqueness theorem is proved in an interval of time independent of c>c0 and conditions are given such that in the limit c→+∞ the solutions converge, in a suita...

We will mainly consider the Sinh-Gordon model in finite spacial volume which corresponds to imposing the periodic boundary conditions φ(x + R) = φ(x). A lot is known about the Sinh-Gordon model in infinite volume R → ∞, see e.g. [1, 2, 3, 4, 5]. The spectrum contains a single particle with mass m which is related to the parameter μ in (1.1) in a definite way [6], see eqn. (5.32) below. The S-ma...