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search.filters.applied.f.access: openAccess × Subject: Parabolic equation ×

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Now showing 1 - 4 of 4
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    A note on a parabolic equation with nonlinear dynamical boundary condition
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Sprekels, Jürgen; Wu, Hao
    We consider a semilinear parabolic equation subject to a nonlinear dynamical boundary condition that is related to the so-called Wentzell boundary condition. First, we prove the existence and uniqueness of global solutions as well as the existence of a global attractor. Then we derive a suitable Lojasiewicz-Simon type inequality to show the convergence of global solutions to single steady states as time tends to infinity under the assumption that the nonlinear terms f, g are real analytic. Moreover, we provide an estimate for the convergence rate.
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    Parabolic equations with dynamical boundary conditions and source terms on interfaces
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Elst, A.F.M. ter; Meyries, Martin; Rehberg, Joachim
    We consider parabolic equations with mixed boundary conditions and domain inhomogeneities supported on a lower dimensional hypersurface, enforcing a jump in the conormal derivative. Only minimal regularity assumptions on the domain and the coefficients are imposed. It is shown that the corresponding linear operator enjoys maximal parabolic regularity in a suitable Lp-setting. The linear results suffice to treat also the corresponding nondegenerate quasilinear problems.
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    Asymptotic behavior of a Neumann parabolic problem with hysteresis
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Eleuteri, Michela; Krejčí, Pavel
    A parabolic equation in two or three space variables with a Preisach hysteresis operator and with homogeneous Neumann boundary conditions is shown to admit a unique global regular solution. A detailed investigation of the Preisach memory dynamics shows that the system converges to an equilibrium in the state space of all admissible Preisach memory configurations as time tends to infinity.
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    Second order sufficient optimality conditions for parabolic optimal control problems with pointwise state constraints
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Krumbiegel, Klaus; Rehberg, Joachim
    In this paper we study optimal control problems governed by semilinear parabolic equations where the spatial dimension is two or three. Moreover, we consider pointwise constraints on the control and on the state. We formulate first order necessary and second order sufficient optimality conditions. We make use of recent results regarding elliptic regularity and apply the concept of maximal parabolic regularity to the occurring partial differential equations.