Parabolic problems and boundary integral equations

Mathematical Methods in the Applied Sciences

Volumn 20, Issue 5, 1997, Pages 449-459

  Baderko, Elena A ^a  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

FUNCTIONS; INTEGRAL EQUATIONS; NUMERICAL METHODS; PARTIAL DIFFERENTIAL EQUATIONS;

ANISOTROPIC HOLDER SPACES; BOUNDARY INTEGRAL EQUATIONS; PARABOLIC PROBLEMS;

BOUNDARY VALUE PROBLEMS;

EID: 0031095562     PISSN: 01704214     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1099-1476(19970325)20:5<449::AID-MMA818>3.0.CO;2-E     Document Type: Article

References (21)

1. Arnold, D. N. and Noon, P. J., 'Coercivity of the single layer heat potential', J. Comput. Math. 7, 100-104 (1989).
2. Baderko, E. A., 'On the solution of the first boundary value problem for parabolic equations with the aid of a simple layer potential', Soviet Math. Dokl., 32, 1-3 (1985).
3. Baderko, E. A., 'Solution of a problem with an oblique derivative for a parabolic equation by the method of boundary integral equations', Diff. Equations, 25, 9-14 (1989).
4. Baderko, E. A., "Smoothness of a 2m-parabolic potential of a simple layer', Diff. Equations, 26, 1-7 (1990).
5. Baderko, E. A., 'Boundary value problems for a parabolic equation, and boundary integral equations', Diff. Equations, 28, 15-20 (1992).
6. Baderko, E. A., 'The single-layer potential and Dirichlet problem', Doki RAN, Russia, 339, 1-3 (1994).
7. Cherepova, M. F., 'Solution of a Bitzadze-Samarski problem for a parabolic equation in a noncylindrical domain', Ph.D. thesis, Moscow University, 1987.
8. Costabel, M., 'Boundary integral operators for the heat equation', Integral Equation Oper. Theory 13, 498-552 (1990).
9. Friedman, A., Partial Differential Equations of Parabolic Type, Prentice-Hall. Englewood Cliffs, NJ, é 1964.
10. Gevrey, M., 'Sur les équations aux dérivées partielles du type parabolique', J. Math. Pur. Appl. Ser. 6,9, 4, 305-471 (1913).
11. Holmgren, E., 'Sur une application de l'équation de M. Volterra', Arc. Math. Astr. Fys., 3, 12 (1907)
12. Hsiao, G. C. and Saranen, J., 'Boundary integral solution of the two-dimensional heat equation', Math. Methods in Appl. Sci., 16, 87-114 (1993).
13. Il'in, A. M., Kalashnikov, A. S. and Oleinik, 'Linear second order parabolic equations', Usp. Math. Nauk, SSSR, 17, 3-146 (1962).
14. Kaminin, L. I., 'On Gevrey theory for parabolic equation', Diff. Uravn., SSSR, 8, 1015-1025, (1972).
15. Kaminin, L. I., 'On existence of solutions for Cauchy problem and boundary problems for parabolic equation', Diff. Uravn. SSSR, 24, 445-455, (1988).
16. Ladyzenskaya, O. A., Solonnikov, V. A. and Ural'ceva, N. N., Linear and Quasilinear Equations of Parabolic Type. Translations of the Mathematical Monographs, Vol. 23, American Mathematical Society, Providence, Rhode Island, 1968.
17. Piskorek, A., 'Sur certains problèmes aux limites pour l'équation parabolique dans un domaine non cylindrique', Ann. Pol. Math., 16, 101-116 (1964).
18. Pogorzelski, W., 'Propriét́eś des integrales de l'équation parabolique normale', Ann. Pol. Math., 4, 61-92 (1957).
19. Pogorzelski, W., 'Problèmes aux limites pour l'équation parabolique normale', Ann. Pol. Math., 4, 110-126 (1957).
20. Pogorzelski, W., Integral Equations, Vol. 1, Pergamon Press, Oxford, 1964.
21. Sheveljova, W. N., 'Solution by the integral equation method of contact problems for parabolic equations, Ph.D. thesis, Moscow University, 1994.