Numerical study of a Transmission Problem in Elasticity with kind damping

2025/05/05 by Kaïs Ammari, Ammari, Kais, Vilmos Komornik +5 · 1 citation
Engineering · #34B05 #34D05 #34H05 #Analysis of PDEs (math.AP) #Elasticity and Wave Propagation #FOS: Mathematics #Geotechnical and Geomechanical Engineering #Optimization and Control (math.OC) #Vibration and Dynamic Analysis

paper · doi:10.48550/arxiv.2505.03043

openalex publication_date 2025/05/05 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28

Abstract

We investigate a transmission problem featuring a specific type of damping. Our primary focus is on analyzing the asymptotic behavior of the associated semigroup, (\mathcal S_{\mathcal A}(t))_{t≥ 0}. We demonstrate that this semigroup exhibits a polynomial rate of decay towards zero when the initial data is taken over the domain \mathcal D(\mathcal A). Furthermore, we establish that this decay rate is optimal. To support our theoretical findings, we present a comprehensive numerical study that validates and illustrates the sharpness of the obtained decay rates.

Citations

• Fine scales of decay of operator semigroups
• Optimal polynomial decay of functions and operator semigroups
• Exponential Decay of Energy of the Euler--Bernoulli Beam with Locally Distributed Kelvin--Voigt Damping
• Sharp Sufficient Conditions for the Observation, Control, and Stabilization of Waves from the Boundary
• Exponential Decay of Energy of Evolution Equations with Locally Distributed Damping
• Fractional order Volterra equations with applications to elasticity
• A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type

Cited by

• Numerical stabilization for a mixture system with kind damping

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