# Degenerate parabolic equation

From Encyclopedia of Mathematics

A partial differential equation

where the function has the following property: For some even natural number , all roots of the polynomial

have non-positive real parts for all real and, for certain , , , and , for some root , or for certain , and the leading coefficient at vanishes. Here is an independent variable which is often interpreted as time; is an -dimensional vector ; is the unknown function; is a multi-index ; is the vector with components

is a vector with components , is an -dimensional vector , and . See also Degenerate partial differential equation, and the references given there.

**How to Cite This Entry:**

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

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Degenerate_parabolic_equation&oldid=18826

This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098