Degenerate hyperbolic equation
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.
Degenerate hyperbolic equation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Degenerate_hyperbolic_equation&oldid=17807