Non-Hyperbolic Solutions to Tangle Equations Involving Composite Links

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...

Solutions of Nonlinear Hyperbolic Equations at Resonance

Speed of wave-front solutions to hyperbolic reaction-diffusion equations.

The asymptotic speed problem of front solutions to hyperbolic reaction-diffusion (HRD) equations is studied in detail. We perform linear and variational analyses to obtain bounds for the speed. In contrast to what has been done in previous work, here we derive upper bounds in addition to lower ones in such a way that we can obtain improved bounds. For some functions it is possible to determine ...

Discontinuous Galerkin method for hyperbolic equations involving δ - functions 1

In this paper, we develop and analyze discontinuous Galerkin (DG) methods to solve hyperbolic equations involving δ-functions. We investigate negative-order norm error estimates for the accuracy of DG approximations to linear hyperbolic conservation laws in one space dimension with singular initial data. We prove that, by using piecewise k-th degree polynomials, at time t, the error in the H(R\...

Thurston’s Spinning Construction and Solutions to the Hyperbolic Gluing Equations for Closed Hyperbolic 3–manifolds

We show that the hyperbolic structure on a closed, orientable, hyperbolic 3–manifold can be constructed from a solution to the hyperbolic gluing equations using any triangulation with essential edges. The key ingredients in the proof are Thurston’s spinning construction and a volume rigidity result attributed by Dunfield to Thurston, Gromov and Goldman. As an application, we show that this give...