Convergence to equilibrium for the semilinear parabolic equation with dynamical boundary condition
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keywords
boundaryconditionconvergencedynamicalequationequilibriumparabolicsemilinear
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This paper is concerned with the asymptotic behavior of the solution to the semilinear parabolic equation with dynamical boundary condition. Our main goal is to prove the convergence of a global solution to an equilibrium as time goes to infinity by means of a suitable \L ojasiewicz--Simon type inequality.
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