The Fuchsian approach to global existence for hyperbolic equations

A VARIATIONAL APPROACH TO THE EXISTENCE OF INFINITELY MANY SOLUTIONS FOR DIFFERENCE EQUATIONS

The existence of infinitely many solutions for an anisotropic discrete non-linear problem with variable exponent according to p(k)–Laplacian operator with Dirichlet boundary value condition, under appropriate behaviors of the non-linear term, is investigated. The technical approach is based on a local minimum theorem for differentiable functionals due to Ricceri. We point out a theorem as a spe...

Hyperbolic Trapped Rays and Global Existence of Quasilinear Wave Equations

The purpose of this paper is to give a simple proof of global existence for quadratic quasilinear Dirichlet-wave equations outside of a wide class of compact obstacles in the critical case where the spatial dimension is three. Our results improve on earlier ones in Keel, Smith and Sogge [9] in several ways. First, and most important, we can drop the star-shaped hypothesis and handle non-trappin...

Global solutions to hyperbolic Navier-Stokes equations

We consider a hyperbolicly perturbed Navier-Stokes initial value problem in R, n = 2, 3, arising from using a Cattaneo type relation instead of a Fourier type one in the constitutive equations. The resulting system is a hyperbolic one with quasilinear nonlinearities. The global existence of smooth solutions for small data is proved, and relations to the classical Navier-Stokes systems are discu...

Complex hyperbolic quasi-Fuchsian groups

A complex hyperbolic quasi-Fuchsian group is a discrete, faithful, type preserving and geometrically finite representation of a surface group as a subgroup of the group of holomorphic isometries of complex hyperbolic space. Such groups are direct complex hyperbolic generalisations of quasi-Fuchsian groups in three dimensional (real) hyperbolic geometry. In this article we present the current st...

Global Existence for Quasilinear Dispersive Equations