I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2006, VOLUME 12, NUMBER 4, PAGES 113-132
Decay of the solution of the first mixed problem for a high-order
parabolic equation with minor terms
L. M. Kozhevnikova
F. Kh. Mukminov
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In a cylindric domain , where is an unbounded domain,
the first mixed problem for a high-order parabolic equation
The boundary values are homogeneous and the initial value is a finite
In terms of new geometrical characteristic of domain, the upper
estimate of -norm
solution to the problem is established.
In particular, in domains
, , under the assumption that the upper an
lower symbols of the operator are separated from zero,
this estimate takes the form
This estimate is determined by minor terms of the equation.
The sharpness of the estimate for the wide class of unbounded domains
is proved in the case .
Last modified: February 17, 2007