TY - GEN A1 - Sprekels, Jürgen A1 - Wu, Hao T1 - A note on a parabolic equation with nonlinear dynamical boundary condition N2 - We consider a semilinear parabolic equation subject to a nonlinear dynamical boundary condition that is related to the so-calles 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. KW - parabolic equation KW - dynamical boundary condition KW - global attractor KW - convergence to equilibrium KW - Lojasiewicz-Simon inequality Y1 - 2012 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/1070 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-10709 ER -