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Browsing by Subject "monotone iterative method"

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    Item type:Article, Access status: Open Access ,
    Stability of solutions of infinite systems of nonlinear differential-functional equations of parabolic type
    (2006) Zabawa, Tomasz
    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.