Indirect stabilization of weakly coupled systems with hybrid boundary conditions | Zendy

Fatiha AlabauBoussouira | Zendy; Piermarco Cannarsa | Zendy; Roberto Guglielmi | Zendy

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Indirect stabilization of weakly coupled systems with hybrid boundary conditions

Author(s) -

Fatiha AlabauBoussouira,

Piermarco Cannarsa,

Roberto Guglielmi

Publication year - 2011

Publication title -

mathematical control and related fields

Language(s) - English

Resource type - Journals

eISSN - 2156-8472

pISSN - 2156-8499

DOI - 10.3934/mcrf.2011.1.413

Subject(s) - mathematics , boundary value problem , boundary (topology) , dirichlet distribution , dirichlet boundary condition , mathematical analysis , compatibility (geochemistry) , robin boundary condition , wave equation , coupling (piping) , mixed boundary condition , mechanical engineering , geochemistry , engineering , geology

We investigate stability properties of indirectly damped systems\udof evolution equations in Hilbert spaces, under new compatibility assumptions.\udWe prove polynomial decay for the energy of solutions and optimize our results\udby interpolation techniques, obtaining a full range of power-like decay rates.\udIn particular, we give explicit estimates with respect to the initial data. We\uddiscuss several applications to hyperbolic systems with hybrid boundary conditions,\udincluding the coupling of two wave equations subject to Dirichlet and\udRobin type boundary conditions, respectively

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