# Degenerate hyperbolic equation

From Encyclopedia of Mathematics

A partial differential equation

(*) |

where the function satisfies the following condition: The roots of the polynomial

are real for all real , and there exist , , , and for which some of the roots either coincide or the coefficient of vanishes. Here is an independent variable which is often interpreted as time; is an -dimensional vector ; is the unknown function; and are multi-indices, , ; is a vector with components

only derivatives of an order not exceeding enter in equation (*); the are the components of a vector ; is an -dimensional vector ; and .

See also Degenerate partial differential equation and the references given there.

**How to Cite This Entry:**

Degenerate hyperbolic equation. A.M. Il'in (originator),

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Degenerate_hyperbolic_equation&oldid=17807

This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098