Global time estimates of L −Lq norms of solutions to general strictly hyperbolic partial differential equations are considered. The case of special interest in this paper are equations exhibiting the dissipative behaviour. Results are applied to discuss time decay estimates for Fokker-Planck equations and for wave type equations with negative mass.

We consider the problem of constructing systems of hyperbolic conservation laws in one space dimension with prescribed eigencurves. This yields an overdetermined system of equations for the eigenvalues-to-be. These equations are analyzed with techniques from exterior differential systems.

We analyze some recent developments in studying discontinuous solutions to nonlinear evolutionary partial differential equations. The central problems include the existence, compactness, and large-time behavior of discontinuous solutions. The nonlinear equations we discuss include nonlinear hyperbolic systems of conservation laws (especially the compressible Euler equations) and the compressibl...

Adomian decomposition method has been applied to solve many functional equations so far. In this work, this method is applied to solve hyperbolic partial differential equations and results will be compared with characteristics method. 2004 Elsevier Inc. All rights reserved.

In this paper, we consider a non-isothermal, non-Newtonian injection process. This leads to the study of a novel elliptic–hyperbolic system. The hyperbolic nature of the system arises because we replace the infinite speed of propagation from classical, thermal elasticity by a finite propagation velocity. We present a formal derivation of the elliptic–hyperbolic system starting from conservation...

This article presents Navier type closed-form solutions for static bending, elastic buckling and free vibration analysis of symmetric functionally graded (FG) sandwich beams using a hyperbolic shear deformation theory. The beam has FG skins and isotropic core. Material properties of FG skins are varied through the thickness according to the power law distribution. The present theory accounts fo...

The parareal algorithm is a numerical method to integrate evolution problems on parallel computers. While this algorithm is effective for diffusive problems, its convergence properties are much less favorable for hyperbolic problems. We analyze in this paper a recently proposed variant of the parareal algorithm for hyperbolic problems for the case of systems of second order ordinary differentia...

We consider a coupled PDE system arising in noise reduction problems. In a two dimensional chamber, the acoustic pressure (unwanted noise) is represented by a hyperbolic wave equation. The floor of the chamber is subject to the action of piezo-ceramic patches (smart materials). The goal is to reduce the acoustic pressure by means of the vibrations of the floor which is modelled by a hyperbolic ...

The failure of uniform dependence on the data is an interesting property classical solution for a hyperbolic system. In this paper, we consider map Cauchy problem to 2D viscous shallow water equations, which hyperbolic–parabolic We give new approach studying issue nonuniform initial these equations. prove that not uniformly continuous in Sobolev spaces H s × $H^s\times H^{s}$ > 2 $s>2$ .

In this paper we establish the short-time existence and uniqueness theorem for hyperbolic geometric flow, and prove the nonlinear stability of hyperbolic geometric flow defined on the Euclidean space with dimension larger than 4. Wave equations satisfied by the curvatures are derived. The relation of hypergeometric flow to the Einstein equation and the Ricci flow is