Degenerate parabolic equation

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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:
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098