# Degenerate hyperbolic equation

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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 .