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. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Degenerate_hyperbolic_equation&oldid=46611
Degenerate hyperbolic equation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Degenerate_hyperbolic_equation&oldid=46611
This article was adapted from an original article by A.M. Il'in (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article