Hyperbolic equations and irregularity
Hyperbolic Equations in Uniform Spaces
The paper is devoted to the Cauchy problem for a semilinear damped wave equation in the whole of ℝ ⁿ. Under suitable assumptions a bounded dissipative semigroup of global solutions is constructed in a locally uniform space . Asymptotic compactness of this semigroup and the existence of a global attractor are then shown.
Hyperbolic equations with non-Lipschitz coefficients.
Hyperbolic heat conduction in two semi-infinite bodies in contact
We find, under the viewpoint of the hyperbolic model of heat conduction, the exact analytical solution for the temperature distribution in all points of two semi-infinite homogeneous isotropic bodies that initially are at uniform temperatures and , respectively, suddenly placed together at time and assuming that the contact between the bodies is perfect. We make graphics of the obtained temperature profiles of two bodies at different times and points. And finally, we compare the temperature...
Hyperbolic methods for Einstein's equations.
Hyperbolic operators with non Lipschitz coefficients
Hyperbolic parabolic equations with nonlinearity of Kirchhoff-Carrier type.
Hyperbolic Perturbation Problems Involving Time Derivatives on the Boundars.
Hyperbolic systems equivalent to the wave equation.
Hyperbolic systems of conservation laws.
This is a survey paper, written in the occasion of an invited talk given by the author at the Universidad Complutense in Madrid, October 1998. Its purpose is to provide an account of some recent advances in the mathematical theory of hyperbolic systems of conservation laws in one space dimension. After a brief review of basic concepts, we describe in detail the method of wave-front tracking approximation and present some of the latest results on uniqueness and stability of entropy weak solutions....
Hyperbolic systems of partial differential inclusions
Hyperbolicity of two by two systems with two independent variables
We study the simplest system of partial differential equations: that is, two equations of first order partial differential equation with two independent variables with real analytic coefficients. We describe a necessary and sufficient condition for the Cauchy problem to the system to be C infinity well posed. The condition will be expressed by inclusion relations of the Newton polygons of some scalar functions attached to the system. In particular, we can give a characterization of the strongly...
Hyperbolické systémy, entropie a metoda konečných objemů
Hypoelliptic operators with characteristic variety of codimension two and the wave equation
Hysteresis and Periodic Solutions of Semilinear and Quasilinear Wave Equations.
Identifiability, stability and reconstruction results of point sources by boundary measurements in heteregeneous trees.
We consider the inverse problem of determining point wave sources in heteregeneous trees, extensions of one-dimensional stratified sets. We show that the Neumann boundary observation on a part of the lateral boundary determines uniquely the point sources if the time of observation is large enough. We further establish a conditional stability and give a reconstructing scheme.
Identifiability, stability and reconstruction results of sources by interior measurements.
Identification of a wave equation generated by a string
We show that we can reconstruct two coefficients of a wave equation by a single boundary measurement of the solution. The identification and reconstruction are based on Krein’s inverse spectral theory for the first coefficient and on the Gelfand−Levitan theory for the second. To do so we use spectral estimation to extract the first spectrum and then interpolation to map the second one. The control of the solution is also studied.
Identification of Green’s Functions Singularities by Cross Correlation of Ambient Noise Signals
In this paper we consider the problem of estimating the singular support of the Green’s function of the wave equation by using ambient noise signals recorded by passive sensors. We assume that noise sources emit stationary random signals into the medium which are recorded by sensors. We explain how the cross correlation of the signals recorded by two sensors is related to the Green’s function between the sensors. By looking at the singular support of the cross correlation we can obtain an estimate...
Identification of hysteric control influence operators representing smart actuators. I: Formulation.