Geodesic
The nonlocal Stefan problem for quasilinear parabolic equation
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 128 (2012) no. 3, pp. 8-16 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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J. O. Takhirov; R. N. Turaev. The nonlocal Stefan problem for quasilinear parabolic equation. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 128 (2012) no. 3, pp. 8-16. http://geodesic.mathdoc.fr/item/VSGTU_2012_128_3_a0/

[1] Friedman A., Partial Differential Equations of Parabolic Type, Prentice-Hal, Englewood Cliffs, N.J., 1964, xiv+347 pp. ; Fridman A., Uravneniya s chastnymi proizvodnymi parabolicheskogo tipa, Mir, M., 1968, 428 pp. | MR | Zbl

[2] Meyrmanov A. M., The Stefan problem, Nauka, Sibirsk. Otdel., Novosibirsk, 1986, 240 pp. | MR

[3] Rubinshteyn L. I., The Stefan problem, Zvaygzne, Riga, 1967, 468 pp. | MR

[4] Douglas J., Jr., “A uniqueness theorem for the solution of the Stefan problem”, Proc. Amer. Math. Soc., 8 (1952), 402–408 | DOI | MR

[5] Kyner W. T., “An existence and uniqueness theorem for a nonlinear Stefan problem”, J. Math. and Mech., 8:4 (1959), 483–498 | MR | Zbl

[6] Kruzhkov S. N., “Nonlinear parabolic equations in two independent variables”, Trudy Moskov. Matem. Obshch., 16 (1967), 329–346 | Zbl