Opuscula Math. 26, no. 1 (2006), 173-183
Stability of solutions of infinite systems of nonlinear differential-functional equations of parabolic type
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.