WIAS Preprint No. 1378, (2008)

A note on a parabolic equation with nonlinear dynamical boundary condition



Authors

  • Sprekels, Jürgen
  • Wu, Hao

2010 Mathematics Subject Classification

  • 35B40 35B41 35B45

Keywords

  • Parabolic equation, dynamical boundary condition, global attractor, convergence to equilibrium, Lojasiewicz-Simon inequality

Abstract

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 Łojasiewicz-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.

Appeared in

  • Nonlinear Anal., 72 (2010) pp. 3028--3048.

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