Stability and analyticity for a coupled plate-membrane system with Kelvin-Voigt damping

Bienvenido Barraza Martínez; Jonathan González Ospino; Jairo Hernández Monzón; Bienvenido Barraza Martínez; Jonathan González Ospino; Jairo Hernández Monzón

doi:10.3934/math.2026961

AIMS Mathematics

2026, Volume 11, Issue 8: 23868-23892. doi: 10.3934/math.2026961

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Research article

Stability and analyticity for a coupled plate-membrane system with Kelvin-Voigt damping

Departamento de Matemáticas, Física y Ciencia de Datos, Universidad del Norte, Km. 5 Vía Puerto Colombia, Área Metropolitana de Barranquilla, Colombia

Received: 28 April 2026 Revised: 24 June 2026 Accepted: 26 June 2026 Published: 04 August 2026
MSC : 35M33, 35B35, 35B40, 47D06, 74K15, 74K20

We present an operator-theoretic analysis of a coupled plate-membrane system with Kelvin-Voigt damping. The model consists of an Euler-Bernoulli plate coupled to a membrane through transmission conditions, with Kelvin-Voigt damping mechanisms acting on different components of the system. By formulating the problem within an abstract Hilbert space framework, we prove that the associated operator generates a strongly continuous and analytic semigroup. As a consequence, we derive regularity properties and describe the long-time behavior of solutions, including asymptotic stability results. The analysis relies on semigroup theory and establishes a rigorous functional-analytic framework for coupled elastic systems with Kelvin-Voigt damping, yielding analyticity and long-time stability properties.
- plate-membrane system,
- coupled PDE systems,
- Kelvin-Voigt damping,
- exponential stability,
- analytic semigroup,
- polynomial stability
Citation: Bienvenido Barraza Martínez, Jonathan González Ospino, Jairo Hernández Monzón. Stability and analyticity for a coupled plate-membrane system with Kelvin-Voigt damping[J]. AIMS Mathematics, 2026, 11(8): 23868-23892. doi: 10.3934/math.2026961

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Abstract

We present an operator-theoretic analysis of a coupled plate-membrane system with Kelvin-Voigt damping. The model consists of an Euler-Bernoulli plate coupled to a membrane through transmission conditions, with Kelvin-Voigt damping mechanisms acting on different components of the system. By formulating the problem within an abstract Hilbert space framework, we prove that the associated operator generates a strongly continuous and analytic semigroup. As a consequence, we derive regularity properties and describe the long-time behavior of solutions, including asymptotic stability results. The analysis relies on semigroup theory and establishes a rigorous functional-analytic framework for coupled elastic systems with Kelvin-Voigt damping, yielding analyticity and long-time stability properties.

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