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