On the Generalized Spectrum for Second-Order Elliptic Systems

On the Generalized Spectrum for Second-order Elliptic Systems

We consider the system of homogeneous Dirichlet boundary value problems (*) Liu = A[an(x)u + a\2(x)v], L2V = ti[ai2{x)u + a.22{x)v] in a smooth bounded domain fi C R", where Li and £2 are formally selfadjoint second-order strongly uniformly elliptic operators. Using linear perturbation theory, continuation methods, and the Courant-Hilbert variational eigenvalue characterization, we give a detai...

On the Fuč́ık Spectrum for Elliptic Systems

We propose an extension of the concept of Fuč́ık spectrum to the case of coupled systems of two elliptic equations, we study its structure and some applications. We show that near a simple eigenvalue of the system, the Fuč́ık spectrum consists (after a suitable reparametrization) of two (maybe coincident) 2-dimensional surfaces. Furthermore, by variational methods, parts of the Fuč́ık spectrum whi...

Analytic Solution for Hypersonic Flow Past a Slender Elliptic Cone Using Second-Order Perturbation Approximations

An approximate analytical solution is obtained for hypersonic flow past a slender elliptic cone using second-order perturbation techniques in spherical coordinate systems. The analysis is based on perturbations of hypersonic flow past a circular cone aligned with the free stream, the perturbations stemming from the small cross-section eccentricity. By means of hypersonic approximations for the ...

On the Spectrum of a Class of Second Order Periodic Elliptic Differential Operators

Least Squares for Second Order Elliptic Problems

In this paper we introduce and analyze two least squares methods for second order elliptic di erential equations with mixed boundary conditions These methods extend to problems which involve oblique derivative boundary conditions as well as nonsym metric and inde nite problems as long as the original problem has a unique solution With the methods to be developed Neumann and oblique boundary con...