A hyperbolic equation: the wave equation
Introduction to linear partial differential equations

Article REF: AF162 V1

A hyperbolic equation: the wave equation
Introduction to linear partial differential equations

Author : Gérard DEBEAUMARCHÉ

Publication date: October 10, 1999 | Lire en français

You do not have access to this resource.

Request your free trial access! Free trial

Already subscribed?Log in!

2. A hyperbolic equation: the wave equation

2.1 Vibrating string equation

This was one of the first partial differential equations to be demonstrated.

It was studied in the first half of the 18th century by d'Alembert : $\frac{\partial^{2} u}{\partial t^{2}} = v^{2} \frac{\partial^{2} u}{\partial x^{2}}$

where v denotes the velocity of wave propagation in the string and u (x, t ) the ordinate of the point of abscissa x on the string at time t (this ordinate being...

You do not have access to this resource.

Exclusive to subscribers. 97% yet to be discovered!

You do not have access to this resource. Click here to request your free trial access!

Already subscribed? Log in!

Ongoing reading
A hyperbolic equation: the wave equation

Previous
page Classification of second-order linear p.d.e.

A parabolic equation: the heat equation

Article included in this offer

"Mathematics"

( 165 articles )

Complete knowledge base

Updated and enriched with articles validated by our scientific committees

Services

A set of exclusive tools to complement the resources

View offer details

References

(1) - REINHARD (H.) - Équations différentielles - , Gauthier-Villars.
(2) - REINHARD (H.) - Équations aux dérivées partielles - , Dunod.
(3) - YOSIDA (K.) - Équations différentielles...

You do not have access to this resource.

Exclusive to subscribers. 97% yet to be discovered!

You do not have access to this resource. Click here to request your free trial access!

Already subscribed? Log in!

Outline
Full outline