Opuscula Math. 26, no. 1 (2006), 173-183

Opuscula Mathematica

# Stability of solutions of infinite systems of nonlinear differential-functional equations of parabolic type

Tomasz S. Zabawa

Abstract. A parabolic initial boundary value problem and an associated elliptic Dirichlet problem for an infinite weakly coupled system of semilinear differential-functional equations are considered. It is shown that the solutions of the parabolic problem is asymptotically stable and the limit of the solution of the parabolic problem as $$t\to\infty$$ is the solution of the associated elliptic problem. The result is based on the monotone methods.

Keywords: stability of solutions, infinite systems, parabolic equations, elliptic equations, semilinear differential-functional equations, monotone iterative method.

Mathematics Subject Classification: 35B40, 35B35, 35J65, 35K60.

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• Tomasz S. Zabawa
• AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Kraków, Poland