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Tamtam Proceedings - lamsin

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172 K. Saoudiet∫v(t, x) dxΩest croissante.Comme u est positive ( minorée) et v est bornée ( majorée (corrollaire 2.1)), alors∫1u(t, x) dx Converge|Ω|etΩ∫1v(t, x) dx|Ω|ΩConvergede (3.4) on déduit que :∫1(u(t, x) + v(t, x))dx = 1 ∫|Ω||Ω|alors il vient :ce qui achève la démonstration.Ωc 1 + c 2 = 1 ∫(u 0 + v 0 )dx.|Ω|ΩΩ(u 0 + v 0 )dx4. Bibliographie[1] N. Alikakos, L p -Bounds of Solutions of Reaction-Diffusion Equations.Comm. P. D. E. 4(1979). 827-828.[2] R. Dautray et J. L. Lions, Analyse mathématique et calcul numérique pour les sciences et lestechniques.Volume 3 Masson,1987.[3] P. Fife, Mathematical aspects of reacting and diffusing systems, lecture Notes in Biomathematics,n ◦ =28, Springer (1979).[4] A. Haraux and A.Youkana, On a Result of K.Masuda Concerning Reaction-Diffusion Equations.Tôhoku. Math. J.40 (1988), 159-163.[5] D. Henry, Geometric Theory of Semilinear Parabolic Equations Lecture Notes in Mathematics840, springer-verlag, New-York, 1984.[6] S. L. Hollis , Global Existence and Buondedness in Reaction-Diffusion Systems. Ph. D. Thesis,North Carolina State University (1986).TAMTAM –Tunis– 2005

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