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On the global existence of solutions of a reaction-diffusion equation with exponential nonlinearity


Author: Assia Barabanova
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
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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 [Enhancements On Off] (What's this?)

  • [1] N. D. Alikakos, $ {L^p}$-bounds of solutions of reaction-diffusion equations, Comm. Partial Differential Equations 4 (1979), 827-868. MR 537465 (82g:35050)
  • [2] T. Cazenave and A. Haraux, Introduction aux problèmes d'évolution semilinéaires, Mathématiques & Applications, vol. 1, Ellipses, Paris, 1990. MR 1299976 (95f:35002)
  • [3] A. Haraux and M. Kirane, Estimations $ {C^1}$ pour des problèmes paraboliques non-linéaires, Ann. Fac. Sci. Toulouse 5 (1983), 265-280. MR 747194 (85h:35118)
  • [4] A. Haraux and A. Youkana, On a result of K. Mazuda concerning reaction-diffusion equations, Tôhoku Math. J. 40 (1988), 159-163. MR 927083 (89f:35112)
  • [5] D. Henry, Geometric theory of semilinear parabolic equations, Lecture Notes in Math., vol. 840, Springer-Verlag, Berlin and New York, 1981. MR 610244 (83j:35084)
  • [6] K. Masuda, On the global existence and asymptotic behavior of reaction-diffusion equations, Hokkaido Math. J. 12 (1983), 360-370. MR 719974 (84m:35017)
  • [7] A. Youkana, Thèse de 3ème cycle, Chapitre 3, Université Paris 6, 1986.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1994-1207533-6
Article copyright: © Copyright 1994 American Mathematical Society

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