This article is cited in 1 scientific paper (total in 1 paper)
On a weak (algebraic) extremum principle for a second-order parabolic system
L. A. Kamynin, B. N. Khimchenko
The notion of a weak “algebraic” extremum principle (WAEP) is introduced for second-order parabolic systems. It is based on the representation of the (coefficient) matrix of the system as a sum of matrices that are similar to diagonal matrices and nilpotent matrices, and on the reduction of the system to a single equation. The validity of the WAEP is proved for a rather broad class of second-order parabolic systems with “full mixing”. The WAEP is applied to prove the uniqueness of the solution of the first boundary-value problem for the parabolic systems in question.
PDF file (1515 kB)
Izvestiya: Mathematics, 1997, 61:5, 933–959
MSC: 35K50, 35B50
L. A. Kamynin, B. N. Khimchenko, “On a weak (algebraic) extremum principle for a second-order parabolic system”, Izv. RAN. Ser. Mat., 61:5 (1997), 35–62; Izv. Math., 61:5 (1997), 933–959
Citation in format AMSBIB
\by L.~A.~Kamynin, B.~N.~Khimchenko
\paper On a~weak (algebraic) extremum principle for a~second-order parabolic system
\jour Izv. RAN. Ser. Mat.
\jour Izv. Math.
Citing articles on Google Scholar:
Related articles on Google Scholar:
This publication is cited in the following articles:
L. I. Kamynin, B. N. Khimchenko, “A priori estimates for the solution of the first boundary-value problem for a class of second-order parabolic systems”, Izv. Math., 65:4 (2001), 705–726
|Number of views:|