We consider singularly perturbed reaction-diffusion equations with singularly perturbed Neumann boundary conditions. We establish the existence of a time-periodic solution u(x, t, ε) with boundary layers and derive conditions for their asymptotic stability The boundary layer part of u(x, t, ε) is of order one, which distinguishes our case from the case of regularly perturbed Neumann boundary co...

For a compact manifold with boundary X we introduce the n-fold scattering stretched product Xn sc which is a compact manifold with corners for each n; coinciding with the previously known cases for n = 2; 3: It is constructed by iterated blow up of boundary faces and boundary faces of multi-diagonals in Xn: The resulting space is shown to map smoothly, by a bbration, covering the usual projecti...

For a compact manifold with boundary X we introduce the n-fold scattering stretched product Xn sc which is a compact manifold with corners for each n, coinciding with the previously known cases for n = 2, 3. It is constructed by iterated blow up of boundary faces and boundary faces of multi-diagonals in Xn. The resulting space is shown to map smoothly, by a b-fibration, covering the usual proje...

We consider the van der Waals’ free energy functional, with scaling parameter ε, in the plane domain R+ × R+, with inhomogeneous Dirichlet boundary conditions. We impose the two stable phases on the horizontal boundaries R+×{0} and R+×{∞}, and free boundary conditions on {∞}×R+. Finally, the datum on {0} ×R+ is chosen in such a way that the interface between the pure phases is pinned at some po...

Using the critical point theory of Szulkin (1986), we study elliptic problems with unilateral boundary conditions and discontinuous nonlinearities. We do not use the method of upper and lower solutions. We prove two existence theorems: one when the right-hand side is nondecreasing and the other when it is nonincreasing. 1. Introduction. In this paper, using the critical-point theory of Szulkin ...

Recent advances in the implementation of spatial econometrics model estimation techniques have made it desirable to compare results, which should correspond between implementations across software applications for the same data. These model estimation techniques are associated with methods for estimating impacts (emanating effects), which are also presented and compared. This review constitutes...

This paper examines the minimum cover of a digital disk by concentric digital circles. If we take the existing definition of the digital circle, then we show a strict lower and upper bound on the size of the cover. We also generate a min-cover which achieves this lower bound. Now one of the minor boundary conditions of generating a digital circle is redefined. For this new definition, an asympt...

A numerical and analytical study of the free convection thermal boundary layer or wall jet at nite Prandtl number is performed to understand the mechanisms of the separation of a high Prandtl number thermal boundary layer ows The model is that adopted by Smith Duck in which the upstream in uence delineates the ow into a double deck structure with the lower deck having thickness O R R being the ...

In this short note, we describe a steady-state solution of full y comp ress ible convection wh ich cou ld be used for comparisons wit h those obtained with the lat ti ce gas approach. T his solution has been obtained wi th a pse udospectral code. It consists of two steady rolls at a maximum Mach number of 0.60 an d at a maximum Reynolds numbe r of 700 . Slip boundary cond it ions for the veloci...