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Browsing by Subject "elliptic equations"

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  • thumbnail.journal.alt
    Item type:Article, Access status: Open Access ,
    Dynamic programming approach to structural optimization problem - numerical algorithm
    (2014) Fulmański, Piotr; Nowakowski, Andrzej; Pustelnik, Jan
    In this paper a new shape optimization algorithm is presented. As a model application we consider state problems related to fluid mechanics, namely the Navier-Stokes equations for viscous incompressible fluids. The general approach to the problem is described. Next, transformations to classical optimal control problems are presented. Then, the dynamic programming approach is used and sufficient conditions for the shape optimization problem are given. A new numerical method to find the approximate value function is developed.
  • thumbnail.journal.alt
    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.
  • thumbnail.journal.alt
    Item type:Article, Access status: Open Access ,
    The maximum principle for viscosity solutions of elliptic differential functional equations
    (2013) Karpowicz, Adrian
    This paper is devoted to the study of the maximum principle for the elliptic equation with a deviated argument. We will consider viscosity solutions of this equation.