In this paper, we study the logarithmic stability for the hyperbolic equations by arbitrary boundary observation. Based on Carleman estimate, we first prove an estimate of the resolvent operator of such equation. Then we prove the logarithmic stability estimate for the hyperbolic equations without any assumption on an observation sub-boundary.

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

in this paper, an effective technique is proposed to determine thenumerical solution of nonlinear volterra-fredholm integralequations (vfies) which is based on interpolation by the hybrid ofradial basis functions (rbfs) including both inverse multiquadrics(imqs), hyperbolic secant (sechs) and strictly positive definitefunctions. zeros of the shifted legendre polynomial are used asthe collocatio...

Optical Aharonov-Bohm effect: an inverse hyperbolic problems approach. Abstract We describe the general setting for the optical Aharonov-Bohm effect based on the inverse problem of the identification of the coefficients of the governing hyperbolic equation by the boundary meas-rements. We interpret the inverse problem result as a possibility in principle to detect the optical Aharonov-Bohm effe...

Kinetic and hyperbolic equations contain small scales (mean free path/time, Debye length, relaxation or reaction time, etc.) that lead to various different asymptotic regimes, in which the classical numerical approximations become prohibitively expensive. Asymptotic-preserving (AP) schemes are schemes that are efficient in these asymptotic regimes. The designing principle of AP schemes are to p...

We show that nonuniqueness of the Leray-Hopf solutions of the Navier-Stokes equation on the hyperbolic plane (2) observed by Chan and Czubak is a consequence of the Hodge decomposition. We show that this phenomenon does not occur on (n) whenever n ≥ 3. We also describe the corresponding general Hamiltonian framework of hydrodynamics on complete Riemannian manifolds, which includes the hyperboli...

We present some global properties of Kaluza-Klein metrics. We state that the Kaluza-Klein metrics associated to globally hyperbolic spacetimes are globally hyperbolic. Applications to the solutions of the relativistic Lorentz equation are shown. (~) 2004 Elsevier Ltd. All rights reserved.

In [1] a hyperbolic analogue of pseudoanalytic function theory was developed. In the present contribution we show that one of the central objects of the inverse problem method the Zakharov-Shabat system is closely related to a hyperbolic Vekua equation for which among other results a generating sequence and hence a complete system of formal powers can be constructed explicitly.

The bidirectional wave transformation developed for scalar equations is shown to have interesting extensions for first-order hyperbolic systems. Assuming a localized waveform of the solution gives an equation for the envelope of the localized wave. The type of the envelope equation depends on the characteristics of the original hyperbolic equations, and the speed of the localized wave. This met...

We prove the convergence, in some strong sense, of a Markov process called “a misanthrope process” to the entropy weak solution of a one-dimensional scalar nonlinear hyperbolic equation. Such a process may be used for the simulation of traffic flows. The convergence proof relies on the uniqueness of entropy Young measure solutions to the nonlinear hyperbolic equation, which holds for both the b...