Article Dans Une Revue Acta Applicandae Mathematicae Année : 2020

Existence, Uniqueness and Stabilization of Solutions of a Generalized Telegraph Equation on Star Shaped Networks

Résumé

The existence, uniqueness, strong and exponential stability of a generalized telegraph equation set on one dimensional star shaped networks are established. It is assumed that a dissipative boundary condition is applied at all the external vertices and an improved Kirchhoff law at the common internal vertex is considered. First, using a general criteria of Arendt-Batty (see Arendt and Batty in Trans. Am. Math. Soc. 306(2):837-852, 1988), combined with a new uniqueness result, we prove that our system is strongly stable. Next, using a frequency domain approach, combined with a multiplier technique and the construction of a new multiplier satisfying some ordinary differential inequalities, we show that the energy of the system decays exponentially to zero.

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hal-04304997 , version 1 (24-11-2023)

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Alaa Hayek, Serge Nicaise, Zaynab Salloum, Ali Wehbe. Existence, Uniqueness and Stabilization of Solutions of a Generalized Telegraph Equation on Star Shaped Networks. Acta Applicandae Mathematicae, 2020, 170 (1), pp.823-851. ⟨10.1007/s10440-020-00360-8⟩. ⟨hal-04304997⟩
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