Parabolic equation on the Riemann manifold

V. Bondarenko

The article describes an approach to solution of partial derivative parabolic equation that generalizes the known parametrix method. The iteration technique proposed exhibits faster convergence than the classical approach.

1. Friedman A. Partial differential equation of parabolic type.— Prentice Hall, Englewood Cliffs, 1964.

2. Varadham S.R.S. On the behavior of the fundamental solution of the heat equation with variable coefficients Comm. Pure Appl. Math.– 1967.– V.20, 194 2.– P.431–455.

3. Gromol D., Klingenberg W., Meyer W. Riemannsche Geometrie im Gro en.— Lecture Notes, 55.– Springer Verlag, 1968.

4. Bondarenko V.G. Diffusion sur variété de courbure non positive Comptes Rendus A.S. – V.324, 194 10.– P.1099–1103.

	Parabolic equation on the Riemann manifold
Author	V. Bondarenko Department of Applied Mathematics, National Technical University of Ukraine “Kyiv Polytechnic Institute”.
Abstract	The article describes an approach to solution of partial derivative parabolic equation that generalizes the known parametrix method. The iteration technique proposed exhibits faster convergence than the classical approach.
Keywords	parabolic partial differential equation, parametrix method, iteration technique
DOI	doi:10.30970/ms.10.1.93-96
Reference	1. Friedman A. Partial differential equation of parabolic type.— Prentice Hall, Englewood Cliffs, 1964. 2. Varadham S.R.S. On the behavior of the fundamental solution of the heat equation with variable coefficients Comm. Pure Appl. Math.– 1967.– V.20, 194 2.– P.431–455. 3. Gromol D., Klingenberg W., Meyer W. Riemannsche Geometrie im Gro en.— Lecture Notes, 55.– Springer Verlag, 1968. 4. Bondarenko V.G. Diffusion sur variété de courbure non positive Comptes Rendus A.S. – V.324, 194 10.– P.1099–1103.
Pages	93-96
Volume	10
Issue	1
Year	1998
Journal	Matematychni Studii
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