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The Cauchy problem for a system of quasilinear parabolic equations of chemical kinetics type

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Abstract

The Cauchy problem for the class of quasilinear parabolic systems of reaction—diffusion type is considered. Under appropriate assumptions regarding the nonlinearities and the initial functions, the nonlocal solvability of this problem and the stabilization of its solution, uniform with respect to the space variables, are established.

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Literature Cited

  1. D. A. Frank-Kamenetskii, Diffusion and Heat Transfer in Chemical Kinetics [in Russian], Izd. Akad. Nauk SSSR, Moscow (1947).

    Google Scholar 

  2. A. Friedman, Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs (1964).

    Google Scholar 

  3. Ya. I. Kanel’, "On nonstationary reaction—diffusion processes," in: The Mathematical Modeling of Nonstationary Problems of Continuous Mechanics [in Russian], Nauka, Moscow (1986), pp. 98–106.

    Google Scholar 

  4. S. N. Kruzhkov and A. N. Peregudov, "The Cauchy problem for a system of equations of chemical kinetics: solvability and asymptotic behavior of the solutions as t → + ∞," Dinamika Sploshn. Sredy, No. 53, 53–55 (1981).

    Google Scholar 

  5. S. N. Kruzhkov and A. N. Peregudov, "The stabilization of the solutions of certain quasilinear parabolic systems," Usp. Mat. Nauk,42, No. 4, 119 (1987).

    Google Scholar 

  6. J. Szarski, Differential Inequalities, PWN - Polish Scientific Publishers, Warszawa (1965).

    Google Scholar 

  7. S. D. Eidel'man, Parabolic Systems, North-Holland, Amsterdam (1969).

    Google Scholar 

  8. A. N. Peregudov, "The second boundary value problem for quasilinear parabolic systems of chemical kinetics type," Zh. Vychisl. Mat. Mat. Fiz.,21, No. 1, 18–28 (1981).

    Google Scholar 

  9. A. N. Peregudov, "On the asymptotic behavior of the solution of the second boundary value problem for a quasilinear parabolic system of chemical kinetics," Izv. Akad. Nauk SSSR, Ser. Mat.,45, No. 1, 227–238 (1981).

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Authors
  1. S. N. Kruzhkov
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  2. A. N. Peregudov
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Additional information

Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 16, pp. 242–261, 1992.

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Kruzhkov, S.N., Peregudov, A.N. The Cauchy problem for a system of quasilinear parabolic equations of chemical kinetics type. J Math Sci 69, 1110–1125 (1994). https://doi.org/10.1007/BF01254397

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  • DOI: https://doi.org/10.1007/BF01254397

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