This paper deals with the boundary value problem involving the differential equation ell y:=-y''+qy=lambda y, subject to the eigenparameter dependent boundary conditions along with the following discontinuity conditions y(d+0)=a y(d-0), y'(d+0)=ay'(d-0)+b y(d-0). In this problem q(x), d, a , b are real, qin L^2(0,pi), din(0,pi) and lambda is a parameter independent of x. By defining a new...

By discovering that solutions of the vanishing viscosity approximation (but without flux regularization) to a scalar conservation law with discontinuous flux are equal to a flux crossing point at the interface, we derive entropy conditions which provide well-posedness to a corresponding Cauchy problem. We assume that the flux is such that the maximum principle holds, but we allow multiple flux ...

The modeling and simulation of electromagnetic wave propagation is often accompanied by a restriction to bounded domains which requires the introduction of artificial boundaries. The corresponding boundary conditions should be chosen in order to minimize parasitic reflections. In this paper, we investigate a new type of transparent boundary condition for a discontinuous Galerkin Trefftz finite ...

For classical regular two-point self-adjoint Sturm-Liouville problems (SLP) the dependence of the eigenvalues on the boundary conditions is well understood because of some surprisingly recent results. Recently there has been a lot of interest in problems with discontinuous boundary conditions. Such conditions are known by various names including transmission conditions, interface conditions, po...

RÉSUMÉ. Sous les hypothèses requises, on étudie une version discontinue des lois de contrôle dites “amortissantes” ou encore “de Jurdjevic-Quinn”. On présente un résultat de stabilisation pratique lorsque la borne sur les contrôles est suffisamment petite. La motivation est d’estimer sa croissance du temps qu’il faut pour atteindre un voisinage donné de la cible quand la susdites borne tend ver...

We consider discontinuous signature change with the weak junction condition favoured by Ellis et. al. [4]. We impose certain regularity conditions and investigate the space of solutions (considered as one-parameter families of three-dimensional Riemannian manifolds) for dust and scalar field models. PACS numbers: 04.20.Cv