A note on parabolic equation with nonlinear dynamical boundary condition

作者：Sprekels Juergen; Wu Hao^*

来源：Nonlinear Analysis-Theory Methods & Applications, 2010, 72(6): 3028-3048.

DOI：10.1016/j.na.2009.11.043

• Parabolic equation
• Dynamical boundary condition
• Global attractor
• Convergence to equilibrium
• Lojasiewicz-Simon inequality

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.

• 出版日期2010-3-15
• 单位复旦大学