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A note on parabolic equation with nonlinear dynamical boundary condition

✍ Scribed by Jürgen Sprekels; Hao Wu

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
1012 KB
Volume
72
Category
Article
ISSN
0362-546X

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✦ Synopsis

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.

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