References
A. S. Kalashnikov, “Some questions of the qualitative theory of nonlinear degenerate parabolic equations of second order,” Uspekhi Mat. Nauk,42, No. 2, 135–176 (1987).
V. A. Galaktionov, S. P. Kurdyumov, and A. A. Samarskii, “On asymptotic eigenfunctions of the Cauchy problem for a certain nonlinear parabolic equation,” Mat. Sb.,126, No. 4, 435–472 (1985).
A. S. Kalashnikov, “On the character of perturbation propagation in nonlinear heat conduction problems with absorption,” Zh. Vychisl. Matematiki i Mat. Fiziki,14, No. 4, 891–905 (1974).
R. Kershner, “On some properties of generalized solutions to quasilinear degenerate parabolic equations,” Acta Math. Hungar.,32, 301–330 (1978).
P. E. Sacks, “The initial and boundary value problem for a class of degenerate parabolic equations,” Comm. Partial Differential Equations,8, No. 7, 693–733 (1983).
M. A. Bertsch, “A class of degenerate diffusion equations with a singular nonlinear term,” Nonlinear Anal. Theory Methods Appl.,7, 117–127 (1983).
L. K. Martinson and K. B. Pavlov, “To the question of spatial localization of thermal perturbations in the theory of nonlinear heat conduction,” Zh. Vychisl. Matematiki i Mat. Fiziki,12, No. 4, 1048–1054 (1972).
U. G. Abdullaev, “Peaking modes in problems for the quasilinear equation of heat and mass transfer with convection,” Zh. Vychisl. Matematiki i Mat. Fiziki,31, No. 3, 462–466 (1991).
U. G. Abdullaev, “On unbounded solutions to the nonlinear heat equation with a sink,” Zh. Vychisl. Matematiki i Mat. Fiziki,32, No. 8, 1244–1257 (1992).
U. G. Abdullaev, “On the localization of unbounded solutions to the nonlinear heat equation with transfer,” Dokl. RAN,329, No. 5, 535–537 (1993).
U. G. Abdullaev, “Large time behavior of solution of the nonlinear infiltration equation,” Nonlinear Anal. Theory Methods Appl.,23, No. 10, 1353–1364 (1994).
U. G. Abdullaev, “On existence of unbounded solutions to the nonlinear heat equation with a sink,” Zh. Vychisl. Matematiki i Mat. Fiziki,33, No. 2, 232–245 (1993).
R. Kershner, “On the behavior of temperature fronts in media with nonlinear heat conductivity in the presence of absorption,” Vestn. Moskov. Univ. Ser. I Mat. Mekh., No. 5, 44–51 (1978).
R. Kershner, “On the behavior of temperature fronts in media with nonlinear heat conductivity in the presence of absorption. II,” Acta Math. Hungar.,35, 13–22 (1980).
L. D. Pokrovskii and S. N. Taranenko, “On conditions for the spatial localization to solutions of the nonlinear heat equation,” Zh. Vychisl. Matematiki i Mat. Fiziki,22, No. 3, 747–751 (1982).
S. Kamin and P. Rosenau, “Thermal waves in an absorbing and convecting medium,” Physica. Ser. D. 1983. V. 8. N 1–2. P. 273–283.
S. N. Antontsev and S. I. Shmarev, “The local energy method and vanishing of weak solutions to nonlinear parabolic equations,” Dokl. Akad. Nauk SSSR,318, No. 4, 777–781 (1991).
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Translated fromSibirskii Matematicheskii Zhurnal, Vol. 36, No. 5, pp. 975–991, September–October, 1995.
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Abdullaev, U.G. On asymptotically exact local estimates for compactly-supported solutions to a nonlinear parabolic equation with absorption. Sib Math J 36, 837–852 (1995). https://doi.org/10.1007/BF02112527
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DOI: https://doi.org/10.1007/BF02112527