On a nonlocal problem for nonlinear parabolic equation

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Home Editorial board Publication ethics Peer review guidelines Latest issue All issues Rules for authors Online submission system's guidelines Submit manuscript Contacts Address: Vatutina st. 53, Vladikavkaz, 362025, RNO-A, Russia Phone: (8672)23-00-54 E-mail: rio@smath.ru	DOI: 10.23671/VNC.2014.1.7422 On a nonlocal problem for nonlinear parabolic equation Takhirov J. O. , Turaev R. N. Vladikavkaz Mathematical Journal 2014. Vol. 16. Issue 1. Abstract: A boundary problem for nonlinear parabolic equation with nonlocal boundary conditions is considered. Some a priori estimates are derived to establish the global existence of the solution. Uniqueness and existence theorems are proved. Keywords: non-local problem, apriori estimations, extremum principle, Holder's condition, nonlinear parabolic equation, Shauder's principle, existence and uniqueness of solution Language: Russian Download the full text For citation: Takhirov J. O., Turaev R. N. On a nonlocal problem for nonlinear parabolic equation. Vladikavkazskii matematicheskii zhurnal [Vladikavkaz Math. J.], vol. 16, no. 1, pp.42-49. DOI 10.23671/VNC.2014.1.7422 + References 1. Samarskij A. A., Mihajlov A. P. Matematicheskoe Modelirovanie: Idei. Metody. Primery [Mathematical Modelling: Ideas. Methods. Examples], Moskva, Fizmatlit, 1997, 320 p. (Russian). 2. Samarskij A. A. i dr. Rezhimy s Obostreniem v Zadachah dlja Kvazilinejnyh Parabolicheskih Uravnenij Parabolicheskih Uravnenij, Moskva, Nauka, 1987, 477 p. (Russian). 3. Ladyzhenskaja O. A., Solonnikov V. A., Ural'ceva N. N. Linejnye i Kvazilinejnye Uravnenija Parabolicheskogo Tipa, Moskva, Nauka, 1967, 736 p. (Russian). 4. Kruzhkov S. N. Nonlinear parabolic equations with two independent variable. Tr. Mosk. Mat. Obshh-va [Trans. of the Moscow Math. Society], 1967, vol. 16, pp. 329-346 (Russian). 5. Kruzhkov S. N. Kvazilinejnye parabolicheskie uravnenija i sistemy s dvumja nezavisimymi peremennymi. Tr. Seminara im. I. G. Petrovskogo, 1979, pp. 217-272 (Russian). 6. Fridman A. Uravnenija s Chastnymi Proizvodnymi Parabolicheskogo Tipa [Partial Differential Equations of Parabolic Type], Moskva, Mir, 1968, 428 p. (Russian). 7. Krylov N. V. Nelinejnye Jellipticheskie i Parabolicheskie Uravnenija Vtorogo Porjadka, Moskva, Nauka, 1985, 374 p. 8. Hudjaev S. I. Pervaja kraevaja zadacha dlja nelinejnyh parabolicheskih uravnenij Dokl. AN SSSR, 1963, vol. 149, no. 3, pp. 535-538 (Russian). 9. Nahushev A. M. Uravnenija Matematicheskoj Biologii, Moskva, Vysshaja Shkola, 1995, 301 p. (Russian). The sole copyright holder of the published work is the Founder of the Vladikavkaz Mathematical Journal. The terms of use of this work are governed by an open license (Creative Commons Attribution-NonCommercial 4.0 International). The use of metadata of the scientific article, including the title, abstract, author information, references, identifiers, and other bibliographic description elements for subsequent unrestricted use, is carried out under the terms of the CC BY or CC0 open licenses. ← Contents of issue


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