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

Applicationes Mathematicae (1999)

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

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topBadraoui, 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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- [2] H. Amann, Dual semigroups and second order linear elliptic boundary value problems, Israel J. Math. 45 (1983), 225-254.
- [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] 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] D. Henry, Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Math. 840, Springer, New York, 1981. Zbl0456.35001
- [6] H. Hoshino and Y. Yamada, Asymptotic behavior of global solutions for some reaction-diffusion equations, Funkcial. Ekvac. 34 (1991), 475-490.
- [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] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, New York, 1983.
- [9] F. Rothe, Global Solutions of Reaction-Diffusion Systems, Lecture Notes in Math. 1072, Springer, Berlin, 1984. Zbl0546.35003
- [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] J. Smoller, Shock Waves and Reaction-Diffusion Equations, Springer, Berlin, 1983. Zbl0508.35002

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