Salem, Abdelmalek Invariant regions and global existence of solutions for reaction-diffusion systems with a tridiagonal matrix of diffusion coefficients and nonhomogeneous boundary conditions. (English) Zbl 1166.35338 J. Appl. Math. 2007, Article ID 12375, 15 p. (2007). Summary: The purpose of this paper is the construction of invariant regions in which we establish the global existence of solutions for reaction-diffusion systems (three equations) with a tridiagonal matrix of diffusion coefficients and with nonhomogeneous boundary conditions. Our techniques are based on invariant regions and Lyapunov functional methods. The nonlinear reaction term has been supposed to be of polynomial growth. Cited in 5 Documents MSC: 35K50 Systems of parabolic equations, boundary value problems (MSC2000) 35K55 Nonlinear parabolic equations 35B40 Asymptotic behavior of solutions to PDEs 35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs 35K57 Reaction-diffusion equations Keywords:three equations; Lyapunov functional methods; polynomial growth PDF BibTeX XML Cite \textit{A. Salem}, J. Appl. Math. 2007, Article ID 12375, 15 p. (2007; Zbl 1166.35338) Full Text: DOI EuDML OpenURL References: [1] A. Friedman, “Partial Differential Equations of Parabolic Type,” Prentice-Hall, Englewood Cliffs, NJ, USA, 1964. · Zbl 0144.34903 [2] D. Henry, Geometric Theory of Semilinear Parabolic Equations, vol. 840 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1984. [3] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, vol. 44 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1983. · Zbl 0516.47023 [4] S. Kouachi, “Global existence of solutions for reaction-diffusion systems with a full matrix of diffusion coefficients and nonhomogeneous boundary conditions,” Electronic Journal of Qualitative Theory of Differential Equations, no. 2, pp. 1-10, 2002. · Zbl 0988.35078 [5] J. Smoller, Shock Waves and Reaction-Diffusion Equations, vol. 258 of Fundamental Principles of Mathematical Science, Springer, New York, NY, USA, 1983. · Zbl 0508.35002 [6] S. Kouachi, “Existence of global solutions to reaction-diffusion systems with nonhomogeneous boundary conditions via a Lyapunov functional,” Electronic Journal of Differential Equations, no. 88, pp. 1-13, 2002. · Zbl 1012.35041 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.