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Author: Recke, Lutz × Subject: lower and upper solutions ×

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Now showing 1 - 3 of 3
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    On existence and asymptotic stability of periodic solutions with an interior layer of reaction-advection-diffusion equations
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Nefedov, Nikolai N.; Recke, Lutz; Schneider, Klaus R.
    We consider a singularly perturbed parabolic periodic boundary value problem for a reaction-advection-diffusion equation. We construct the interior layer type formal asymptotics and propose a modified procedure to get asymptotic lower and upper solutions. By using sufficiently precise lower and upper solutions, we prove the existence of a periodic solution with an interior layer and estimate the accuracy of its asymptotics. Moreover, we are able to establish the asymptotic stability of this solution with interior layer.
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    Exponential asymptotic stability via Krein-Rutman theorem for singularly perturbed parabolic periodic Dirichlet problems
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Nefedov, Nikolai N.; Recke, Lutz; Schneider, Klaus R.
    We consider singularly perturbed semilinear parabolic periodic problems and assume the existence of a family of solutions. We present an approach to establish the exponential asymptotic stability of these solutions by means of a special class of lower and upper solutions. The proof is based on a corollary of the Krein-Rutman theorem.
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    Existence and asymptotic stability of a periodic solution with boundary layers of reaction-diffusion equations with singularly perturbed Neumann boundary conditions
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Butuzov, Valentin F.; Nefedov, Nikolai N.; Recke, Lutz; Schneider, Klaus R.
    We consider singularly perturbed reaction-diffusion equations with singularly perturbed Neumann boundary conditions. We establish the existence of a time-periodic solution u(x; t; epsilon) with boundary layers and derive conditions for their asymptotic stability The boundary layer part of u(x; t; ") is of order one, which distinguishes our case from the case of regularly perturbed Neumann boundary conditions, where the boundary layer is of order epsilon.