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

• Autorzy: Salah Badraoui
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

global existence; boundedness; reaction-diffusion equations; large time behaviour

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 1999
• Tom: 26
• Numer: 2
• Strony: 133-150

Daty

wydano

1999

otrzymano

1998-06-15

poprawiono

1998-11-19

Twórcy

autor

Salah Badraoui

• Institut des Sciences Exactes, Université 8 mai 1945, BP. 401, Guelma 24000, Algeria

Bibliografia

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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.
• [4] A. Haraux et M. Kirane, Estimations $C^1$ pour des problèmes paraboliques semi-linéaires, Ann. Fac. Sci. Toulouse 5 (1983), 265-280.
• [5] D. Henry, Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Math. 840, Springer, New York, 1981.
• [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.
• [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.
• [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.