In this study we investigate asymptotic behavior of eigenvalues and eigenfunctions of one discontinuous Sturm-Liouville problem with eigendependent boundary and transmission conditions. c ©2003 Yang’s Scientific Research Institute, LLC. All rights reserved.

A discontinuous Galerkin finite element method has been developed to treat the high-order spatial derivatives appearing in the Cahn–Hilliard equation. The Cahn–Hilliard equation is a fourth-order nonlinear parabolic partial differential equation, originally proposed to model phase segregation of binary alloys. The developed discontinuous Galerkin approach avoids the need for mixed finite elemen...

Abstract. Balancing Neumann-Neumann methods are extented to mixed formulations of the linear elasticity system with discontinuous coeÆcients, discretized with mixed nite or spectral elements with discontinuous pressures. These domain decomposition methods implicitly eliminate the degrees of freedom associated with the interior of each subdomain and solve iteratively the resulting saddle point S...

In this article we apply the volume-perturbation method to systems of particles interacting via discontinuous potentials. We have found that an accurate Monte Carlo simulation protocol can be used in order to study properties of very general non-spherical systems with discontinuous potentials, such as chain molecules and spherocylinders with square-well interactions, and chain molecules with sq...

In practice we frequently encounter systems which are most appropriately represented by discontinuous ordinary differential equations. Such equations are investigated qualitatively by Filippov [Z], He [3], Michel and Porter [S, 61, and others. Many such systems often are complex and of a very large scale. It is possible to view such systems as consisting of several simpler subsystems which when...

This paper is concerned with the quasi-synchronization issue of linearly coupled networks with discontinuous nonlinear functions in each isolated node. Under the framework of Filippov systems, the existence and boundedness of solutions for such complex networks can be guaranteed by the matrix measure approach. A design method is presented for the synchronization controllers of coupled networks ...

We prove the existence of a perfect equilibrium within a class of compact, metric, and possibly discontinuous games. Our conditions for existence are easily verified in a variety of economic games.

We investigate bifurcations in the chain recurrent set for a particular class of one-parameter families of diffeomorphisms in the plane. We give necessary and sufficient conditions for a discontinuous change in the chain recurrent set to occur at a point of heteroclinic tangency. These are also necessary and sufficient conditions for an -explosion to occur at that point.

This paper concerns the construction of a discontinuous parametric curve or surface from a finite set of points and tangent conditions. The method is adapted from the theory of the discrete smoothing variational splines to introduce a discontinuity set and some tangent conditions. Such method is justified by a convergence result.

We compare the properties of several notions of perfectness within classes of compact, metric, and (possibly) discontinuous games, and show that in the presence of payoff discontinuities, standard notions of perfectness may fail a weakening of admissibility termed limit admissibility. We also provide conditions ensuring the existence of a limit admissible perfect equilibrium. These conditions a...