Hyperbolic Partial Differential Equations and Wave Phenomena 0-8218-1021-9, 9780821810217

Table of contents :
Content: Wave Phenomena and Hyperbolic Equations --
Equations of wave phenomena --
The vibration of a string --
The equation of oscillation of a spring --
The equation for the propagation of sound --
Maxwell's equations, elastic equations --
Hyperbolic partial differential operators --
Hyperbolic differential operators --
Problems that we will consider --
Formulae for solutions of an initial value problem for a wave equation --
The Existence of a Solution for a Hyperbolic Equation and its Properties --
Finite propagation speed, domains of dependence and influence --
Energy estimate of the solution --
The domain of dependence --
The domain of influence --
Finite speed of propagation --
An a priori estimate of the solution --
On the premise of results for elliptic equations --
Energy estimate --
An estimate of partial derivatives of higher order --
Elimination of the extra assumption, approximation due a mollifier --
Energy conservation --
Existence of the solution --
The Hille-Yosida theorem --
The operator A --
The existence of a solution for the initial boundary value problem --
Smoothness of the solution --
The Construction of Asymptotic Solutions --
An asymptotic solution of the hyperbolic equation --
The Eikonal equation --
Canonical equations --
The construction of the solution --
The transport equation and the behaviour of the asymptotic solution --
The transport equation --
The behaviour of the asymptotic solution --
The propagation of sound in air in which the temperature is not constant --
The propagation of singularities.

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