Under the condition that unstable manifolds are one dimensional, the derivative formula of the potential function of the generalized SRB measure with respect to the underlying dynamical system is extended from the hyperbolic attractor case to the general case when the hyperbolic set intersecting with unstable manifolds is a Cantor set. It leads to derivative formulas of objects and quantities t...

Nonlocal problems for hyperbolic equations of the first order describe the dynamic of population [1]–[3]. During the last thirty years the existence and uniqueness of the solution of nonlocal problems for the system of hyperbolic equations have been considered in a number of papers [4]–[8]. The authors assumed that the nonlinear functions satisfy the Lipschitz condition with respect to the unkn...

We consider the initial value problem for some nonlinear hyperbolic and dispersive systems in one space dimension. Combining the classical energy method and the smoothing estimates for the Airy equation, we guarantee the time local well-posedness for this system. We also discuss the extension of our results to more general hyperbolic-dispersive system.

We construct an hyperbolic approximation of the Vlasov equation in which the dependency on the velocity variable is removed. The resulting model enjoys interesting conservation and entropy properties. It can be numerically solved by standard schemes for hyperbolic systems. We present numerical results for one-dimensional classical test cases in plasma physics: Landau damping, two-stream instabi...

We investigate viscous shock profiles of the Riemann problem for systems of hyperbolic balance laws. Even strictly hyperbolic flux terms together with a nonoscillating kinetic part can lead to oscillating viscous shock profiles. They appear near a Hopf-like bifurcation point of the traveling wave equation.

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...