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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the global existence of solutions of a reaction-diffusion equation with exponential nonlinearity
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by Assia Barabanova PDF
Proc. Amer. Math. Soc. 122 (1994), 827-831 Request permission

Abstract:

We generalize the result of Haraux and Youkana concerning the global existence of nonnegative solutions of a reaction-diffusion equation with exponential nonlinearity. We also show the asymptotic behavior of the global solutions as $t \to \infty$.
References
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  • Thierry Cazenave and Alain Haraux, Introduction aux problĂšmes d’évolution semi-linĂ©aires, MathĂ©matiques & Applications (Paris) [Mathematics and Applications], vol. 1, Ellipses, Paris, 1990 (French). MR 1299976
  • A. Haraux and M. Kirane, Estimations $C^{1}$ pour des problĂšmes paraboliques semi-linĂ©aires, Ann. Fac. Sci. Toulouse Math. (5) 5 (1983), no. 3-4, 265–280 (French, with English summary). MR 747194
  • Alain Haraux and Amar Youkana, On a result of K. Masuda concerning reaction-diffusion equations, Tohoku Math. J. (2) 40 (1988), no. 1, 159–163. MR 927083, DOI 10.2748/tmj/1178228084
  • Daniel Henry, Geometric theory of semilinear parabolic equations, Lecture Notes in Mathematics, vol. 840, Springer-Verlag, Berlin-New York, 1981. MR 610244
  • KyĂ»ya Masuda, On the global existence and asymptotic behavior of solutions of reaction-diffusion equations, Hokkaido Math. J. 12 (1983), no. 3, 360–370. MR 719974, DOI 10.14492/hokmj/1470081012
    • A. Youkana, ThĂšse de 3Ăšme cycle, Chapitre 3, UniversitĂ© Paris 6, 1986.
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Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 122 (1994), 827-831
  • MSC: Primary 35K57; Secondary 35K50, 35K55
  • DOI: https://doi.org/10.1090/S0002-9939-1994-1207533-6
  • MathSciNet review: 1207533