Geodesic
About Green's function of a parabolic problem on a graph
Vladikavkazskij matematičeskij žurnal, Tome 14 (2012) no. 4, pp. 32-40 
R. Ch. Kulaev. About Green's function of a parabolic problem on a graph. Vladikavkazskij matematičeskij žurnal, Tome 14 (2012) no. 4, pp. 32-40. http://geodesic.mathdoc.fr/item/VMJ_2012_14_4_a4/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The work is devoted to Green's function of the mixed boundary problem for equation of parabolic type on geometrical graph. Existence, continuity and positivity of Green's function are studied.

[1] Ali-Mehmeti F., von Below J. A., Nicaise S., Partial Differential Equations on Multistructures, Proceedings of a Conference (Luminy, France), Ser. Lecture Notes in Pure and Appl. Math., 219, Marcel Dekker, New York, 2001, 256 pp. | MR | Zbl

[2] von Below J. A., “Classical solvability of linear parabolic equations on networks”, J. Diff. Eq., 75 (1998), 316–337 | MR

[3] Gen Qi Xu, Mastorakis N. E., Differential Equations on Metric Graph, WSEAS Press, 2010, 242 pp.

[4] von Below J. A., “A Qualitative theory for parabolic problems under dynamical boundary conditions”, J. of Inequal. and Appl., 5 (2000), 467–486 | MR | Zbl

[5] von Below J. A., “A maximum principle for semilinear parabolic network equations”, Diff. Eq. with Appl. in Biology, Physics and Engineering, M. Dekker Inc., New York, 1991, 37–45 | MR

[6] Pokornyi Yu. V., Penkin O. M., Pryadiev V. L., Borovskikh A. V., Lazarev K. P., Shabrov S. A., Differentsialnye uravneniya na geometricheskikh grafakh, Fizmatlit, M., 2004, 272 pp. | MR | Zbl

[7] Penkin O. M., “O printsipe maksimuma dlya ellipticheskogo uravneniya na dvumernom kletochnom komplekse”, Dokl. AN, 352:4 (1997), 462–465 | MR | Zbl

[8] Penkin O. M., “O printsipe maksimuma dlya ellipticheskogo uravneniya na stratifitsirovannykh mnozhestvakh”, Differents. uravneniya, 34:10 (1998), 1433–1444 | MR

[9] Penkin O. M., Bogatov E. M., “O slaboi razreshimosti zadachi Dirikhle na stratifitsirovannykh mnozhestvakh”, Mat. zametki, 68:6 (2000), 874–876 | DOI | MR | Zbl

[10] Kulaev R. Ch., “O razreshimosti parabolicheskoi zadachi na grafe”, Ufimskii mat. zhurn., 2:4 (2010), 74–85

[11] Kamynin L. I., Maslennikova V. N., “O printsipe maksimuma dlya uravneniya s razryvnymi koeffitsientami”, Sib. mat. zhurn., 2:3 (1961), 384–399 | MR | Zbl

[12] Gilbarg D., Trudinger N., Ellipticheskie differentsialnye uravneniya s chastnymi proizvodnymi vtorogo poryadka, Nauka, M., 1989, 464 pp. | MR | Zbl

[13] Fridman A., Uravneniya s chastnymi proizvodnymi parabolicheskogo tipa, Mir, M., 1969, 427 pp.