In this paper, a discrete version of a reaction-diffusion equation, also known as coupled map lattice (CML), which corresponds to the Turing model of morphogenesis is studied. It is shown that CML possesses a hyperbolic property displaying a type of spatio-temporal chaos. Throughout a mathematical background of hyperbolic properties in lattice dynamical systems which are related to spatio-tempo...

We extend a family of high-resolution, semidiscrete central schemes for hyperbolic systems of conservation laws to three-space dimensions. Details of the schemes, their implementation, and properties are presented together with results from several prototypical applications of hyperbolic conservation laws including a nonlinear scalar equation, the Euler equations of gas dynamics, and the ideal ...

We use an elliptic differential equation of Ţiţeica (or Toda) type to construct a minimal Lagrangian surface in CH from the data of a compact hyperbolic Riemann surface and a cubic holomorphic differential. The minimal Lagrangian surface is equivariant for an SU(2, 1) representation of the fundamental group. We use this data to construct a diffeomorphism between a neighbourhood of the zero sect...

We introduce an operator splitting based stochastic Galerkin method for the one-dimensional compressible Euler equations with random inputs. The method uses a generalized polynomial chaos approximation in the stochastic Galerkin framework (referred to as the gPC-SG method). It is well-known that such approximations for nonlinear system of hyperbolic conservation laws do not necessarily yield gl...

We construct solutions of a free boundary value problem for a hyperbolic equation with Dirichlet boundary data. This problem arises from a model of deformation of granular media.

We obtain a system for the spatial metric and extrinsic curvature of a spacelike slice that is hyperbolic non-strict in the sense of Leray and Ohya and is equivalent to the Einstein equations. Its characteristics are the light cone and the normal to the slice for any choice of lapse and shift functions, and it admits a well-posed causal Cauchy problem in a Gevrey class of index α = 2. The syste...

In this paper, we establish an optimal trace regularity theorem, also known as the hidden regularity theorem [L2], for the anisotropic linear elasticity equation on a bounded domain Ω with Lipschitz boundary. In its simplest form it provides a space-time L estimate for the trace of the normal derivative for the solution. Over the years, such sharp trace regularity theorems have proven to be cru...

The Dirichlet problem and other nonclassical boundary value problems for linear hyperbolic equations with two independent variables have been the subject of various studies (see, e.g., [1]–[8], [10]–[16] and the references therein). However such problems for higher order nonlinear hyperbolic equations still remain unstudied. The present paper is an attempt to fulfill the existing gap. Let m and...

Hot deformation behavior of a medium Cr/Mn Al6061 aluminum alloy was studied by isothermal compression test at temperatures range of 320 to 480 °C and strain rates range of 0.001 to 0.1 s −1. The true stresstrue strain curves were analyzed to characterize the flow stress of Al6061. Plastic behavior, as a function of both temperature and strain rate for Al6061, was also modeled using a hyperboli...