Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 9 (2014), 105 -- 115

GLOBAL EXISTENCE OF SOLUTION FOR REACTION DIFFUSION SYSTEMS WITH A FULL MATRIX OF DIFFUSION COEFFICIENTS

K. Boukerrioua

Abstract. The goal of this work is to study the global existence in time of solutions for some coupled systems of reaction diffusion which describe the spread within a population of infectious disease. We consider a full matrix of diffusion coefficients and we show the global existence of the solutions.

2010 Mathematics Subject Classification: 35K45; 35K57.
Keywords: global existence; reaction diffusion systems; Lyapunov functional.

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References

  1. N. D. Alikakos, Lp-Bounds of Solutions of Reaction-Diffusion Equations, Comm. Partial. Differential. Equations 4 (1979), 827-868. MR0537465. Zbl 0421.35009.

  2. C. Castillo-Chavez, K. Cook, W. Huang and S. A. Levin, On the role of long incubation periods in the dynamics of acquires immunodeficiency syndrome, AIDS, J. Math. Biol. 27 (1989) 373-398. MR1009897. Zbl 0715.92029.

  3. E. L. Cussler, Multicomponent diffusion, Chemical Engineering Monographs 3 Elsevier Scientific Publishing Company, Amsterdam, 1976.

  4. A. Haraux and A.Youkana, On a Result of K. Masuda Concerning Reaction-Diffusion Equations, Tohoku. Math. J. 40 (1988), 159-163. MR0927083. Zbl 0689.35041.

  5. D. Henry, Theory of Semi-Linear Parabolic Equations, Lecture Notes in Math. 840, Springer Verlas, New York, 1984.

  6. S. Kouachi, Global Existence of solutions for reaction-diffusion systems with a full matrix of diffusion coefficients and non homogeneous boundary conditions, Electron. J. Qual. Theory Differ. Equ. 2002, paper no. 2, 10pp. MR1884960. Zbl 0988.35078.

  7. K. Masuda, On the Global Existence and Asymptotic Behavior of Solution of Reaction-Diffusion Equations, Hokaido Math. J. 12 (1983), 360-370. MR0719974. Zbl 0529.35037.

  8. L. Melkemi, A. Z. Mokrane and A. Youkana, On the uniform boundness of the solutions of systems of reaction-diffusion equtions, Electron. J. Qual. Theory Differ. Equ. 2005, paper no. 24, 10pp. MR2191668. Zbl 1090.35095.

  9. A. Pazy, Semigroups of linear operators and applications to partial differential equations, Applied. Math. Sciences 44, Springer-Verlag, New York, 1983. MR0710486. Zbl 0516.47023.

  10. B. Rebai, Global classical solutions for Reaction-Diffusion Systems with a triangular Matrix of Diffusion Coefficients, Electron. J. Differ. Equ. (EJDE) 2011 (2011), paper no. 99, 8pp. MR2832275. Zbl 1227.35151.

  11. J. Savchik, B. Changs and H. Rabitz, Application of moments to the general linear multicomponent reaction-diffusion equations, J. Phys. Chem. 37 (1983), 1990--1997.

  12. J. Smoller, Shock Wavesand Reaction-Diffusion Equations, Springer-Verlag, New York 1983. MR0688146. Zbl 0508.35002.



K. Boukerrioua
University of Guelma, Guelma, Algeria.
E-mail: khaledv2004@yahoo.fr

http://www.utgjiu.ro/math/sma