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In this paper we study linear conservative systems of finite dimension coupled with an infinite dimensional system of diffusive type. Computing the time-derivative of an appropriate energy functional along the solutions helps us to prove the well-posedness of the system and a stability property. But in order to prove asymptotic stability we need to apply a sufficient spectral condition. We also illustrate the sharpness of this condition by exhibiting some systems for which we do not have the asymptotic...
In this paper we study linear conservative systems of finite
dimension
coupled with an infinite dimensional system of diffusive type.
Computing the time-derivative of an
appropriate energy functional along the solutions helps us to
prove the well-posedness of the system
and a stability property.
But in order to prove asymptotic stability we need to apply
a sufficient spectral condition. We also illustrate the sharpness of this
condition by exhibiting some systems for which we do not have the asymptotic
property.
...
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