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

Tyt. z nagł.References p. 182-183.Dostępny również w formie drukowanej.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 --> ∞ 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