Funkcialaj Ekvacioj
Print ISSN : 0532-8721
Remarks on the Decay Rate of the Energy for Damped Modified Boussinesq-Beam Equations on the 1-D Half Line
Ruy Coimbra CharãoRyo Ikehata
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2017 Volume 60 Issue 2 Pages 239-257

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Abstract

We consider the mixed problem for weakly damped modified Boussinesq-Beam equations on the one dimensional half line (0, + ∞). We shall derive fast decay results of the total energy and L2-norm of solutions based on the idea due to [7], which is an essential modification of that developed by Morawetz [15]. In order to apply that idea due to [7] to the one dimensional exterior mixed problem, one also constructs an important Hardy-Sobolev type inequality, which holds only in the 1-D half line case.

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© 2017 by the Division of Functional Equations, The Mathematical Society of Japan
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