Abstract:
In this paper, we deal with free boundary problem with nonlocal boundary condition for quasilinear parabolic equation. For the solutions of the problem apriory estimates of Shauder's type are established. On the base of apriory estimations the existence and uniqueness theorems are proved
Keywords:
nonlocal problem, Stefan problem, quasilinear parabolic equation, free boundary,
priori estimates, existence and uniqueness theorem, fixed boundary, method of potentials, maximum principle.
Original article submitted 10/VIII/2011 revision submitted – 19/XII/2011
Citation:
J. O. Takhirov, R. N. Turaev, “The nonlocal Stefan problem for quasilinear parabolic equation”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 3(28) (2012), 8–16
\Bibitem{TakTur12}
\by J.~O.~Takhirov, R.~N.~Turaev
\paper The nonlocal Stefan problem for quasilinear parabolic equation
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2012
\vol 3(28)
\pages 8--16
\mathnet{http://mi.mathnet.ru/vsgtu1010}
\crossref{https://doi.org/10.14498/vsgtu1010}
\zmath{https://zbmath.org/?q=an:06517515}
Linking options:
https://www.mathnet.ru/eng/vsgtu1010
https://www.mathnet.ru/eng/vsgtu/v128/p8
This publication is cited in the following 3 articles:
M. S. Rasulov, “Zadacha dlya parabolicheskogo uravneniya s dvumya svobodnymi granitsami”, Vestnik KRAUNTs. Fiz.-mat. nauki, 42:1 (2023), 108–121
A. G. Podgaev, V. Ya. Prudnikov, T. D. Kulesh, “Globalnaya razreshimost trekhmernoi osesimmetrichnoi zadachi Stefana dlya kvazilineinogo uravneniya”, Dalnevost. matem. zhurn., 22:1 (2022), 61–75
Petro M. Martynyuk, “Existence and uniqueness of a solution of the problem with free boundary in the theory of filtration consolidation of soils with regard for the influence of technogenic factors”, J. Math. Sci., 207, no. 1, 59–73; Ukr. Mat. Visn., 11:4 (2014), 524–542
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