Abstract
A model equation in the theory of combustion is considered. For this equation, we establish estimates for the instant of thermal explosion, i.e., of the blow-up of the solution, both for the Cauchy problem and for initial boundary-value problems.
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References
I. M. Gelfand, “Some problems of the theory of quasilinear equations,” Uspekhi Mat. Nauk 14(2), 87–158 (1959).
G. I. Barenblatt, Ya. B. Zel’dovich, V. B. Librovich, and G. M. Makhviladze, Mathematical Theory of Combustion and Explosion (Nauka, Moscow, 1980) [in Russian].
D. A. Frank-Kamenetskii, Diffusion and Heat Transfer in Chemical Kinetics (Nauka, Moscow, 1967) [in Russian].
S. I. Khudyaev, Threshold Phenomena in Nonlinear Equations (Fizmatlit, Moscow, 2003) [in Russian].
D.H. Sattinger, “A nonlinear parabolic system in the theory of combustion,” Quart. Appl.Math. 33(1), 47–61 (1975).
É. Mitidieri and S. I. Pokhozhaev, A Priori Estimates and Blow-Up of Solutions to Nonlinear Partial Differential Equations and Inequalities in Trudy Mat. Inst. Steklov (Nauka, Moscow, 2001), Vol. 234 [Proc. Steklov Inst.Math. 234].
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Original Russian Text © S. I. Pokhozhaev, 2010, published in Matematicheskie Zametki, 2010, Vol. 88, No. 1, pp. 53–62.
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Pokhozhaev, S.I. Concerning an equation in the theory of combustion. Math Notes 88, 48–56 (2010). https://doi.org/10.1134/S0001434610070059
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DOI: https://doi.org/10.1134/S0001434610070059