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

Zabawa T.S.

Opuscula Mathematica

2006

Vol. 26, no. 1

173-183

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.

Monotone iteration for infinite systems of parabolic equations

Pudełko A.

Opuscula Mathematica

2005

Vol. 25, no. 2

307-318

In the paper the Cauchy problem for and infinite system of parabolic type equations is studied. The general operators of the parabolic type of second order with variable coefficients are considered and the system is weakly coupled. Among the obtained results there is a theorem on differential inequality as well as the existence and uniqueness theorem in the class of continuous-bounded functions obtained by monotone iterative method.