Behaviour of global solutions for a system of reaction-diffusion equations from combustion theory

Salah Badraoui

Applicationes Mathematicae (1999)

  • Volume: 26, Issue: 2, page 133-150
  • ISSN: 1233-7234

Abstract

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We are concerned with the boundedness and large time behaviour of the solution for a system of reaction-diffusion equations modelling complex consecutive reactions on a bounded domain under homogeneous Neumann boundary conditions. Using the techniques of E. Conway, D. Hoff and J. Smoller [3] we also show that the bounded solution converges to a constant function as t → ∞. Finally, we investigate the rate of this convergence.

How to cite

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Badraoui, Salah. "Behaviour of global solutions for a system of reaction-diffusion equations from combustion theory." Applicationes Mathematicae 26.2 (1999): 133-150. <http://eudml.org/doc/219230>.

@article{Badraoui1999,
abstract = {We are concerned with the boundedness and large time behaviour of the solution for a system of reaction-diffusion equations modelling complex consecutive reactions on a bounded domain under homogeneous Neumann boundary conditions. Using the techniques of E. Conway, D. Hoff and J. Smoller [3] we also show that the bounded solution converges to a constant function as t → ∞. Finally, we investigate the rate of this convergence.},
author = {Badraoui, Salah},
journal = {Applicationes Mathematicae},
keywords = {global existence; boundedness; reaction-diffusion equations; large time behaviour; homogeneous Neumann boundary conditions; rate of convergence},
language = {eng},
number = {2},
pages = {133-150},
title = {Behaviour of global solutions for a system of reaction-diffusion equations from combustion theory},
url = {http://eudml.org/doc/219230},
volume = {26},
year = {1999},
}

TY - JOUR
AU - Badraoui, Salah
TI - Behaviour of global solutions for a system of reaction-diffusion equations from combustion theory
JO - Applicationes Mathematicae
PY - 1999
VL - 26
IS - 2
SP - 133
EP - 150
AB - We are concerned with the boundedness and large time behaviour of the solution for a system of reaction-diffusion equations modelling complex consecutive reactions on a bounded domain under homogeneous Neumann boundary conditions. Using the techniques of E. Conway, D. Hoff and J. Smoller [3] we also show that the bounded solution converges to a constant function as t → ∞. Finally, we investigate the rate of this convergence.
LA - eng
KW - global existence; boundedness; reaction-diffusion equations; large time behaviour; homogeneous Neumann boundary conditions; rate of convergence
UR - http://eudml.org/doc/219230
ER -

References

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  1. [1] N. D. Alikakos, An application of the invariance principle to reaction-diffusion equations, J. Differential Equations 33 (1979), 201-225. Zbl0386.34046
  2. [2] H. Amann, Dual semigroups and second order linear elliptic boundary value problems, Israel J. Math. 45 (1983), 225-254. 
  3. [3] E. Conway, D. Hoff and J. Smoller, Large time behavior of solutions of systems of nonlinear reaction-diffusion equations, SIAM J. Appl. Math. 35 (1978), 1-16. Zbl0383.35035
  4. [4] A. Haraux et M. Kirane, Estimations C 1 pour des problèmes paraboliques semi-linéaires, Ann. Fac. Sci. Toulouse 5 (1983), 265-280. Zbl0531.35048
  5. [5] D. Henry, Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Math. 840, Springer, New York, 1981. Zbl0456.35001
  6. [6] H. Hoshino and Y. Yamada, Asymptotic behavior of global solutions for some reaction-diffusion equations, Funkcial. Ekvac. 34 (1991), 475-490. 
  7. [7] M. Kirane and A. Youkana, A reaction-diffusion system modelling the post irridiation oxydation of an isotactic polypropylene, Demonstratio Math. 23 (1990), 309-321. Zbl0767.35037
  8. [8] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, New York, 1983. 
  9. [9] F. Rothe, Global Solutions of Reaction-Diffusion Systems, Lecture Notes in Math. 1072, Springer, Berlin, 1984. Zbl0546.35003
  10. [10] D. Schmitt, Existence globale ou explosion pour les systèmes de réaction-diffusion avec contrôle de masse, Thèse de doctorat de l'Université Henri Poincaré, Nancy I, 1995. 
  11. [11] J. Smoller, Shock Waves and Reaction-Diffusion Equations, Springer, Berlin, 1983. Zbl0508.35002

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