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The present paper is devoted to the study of exponential stabilization of a one-dimensional thermoelastic diffusion problem of type II for isotropic and homogeneous materials with frictional damping and time delay. The system of equations under consideration is a coupling of three hyperbolic equations involving three variables considering frictional damping and time delay on each variable. Using semigroup theory, we prove the well-posedness by the Lumer–Phillips theorem and the exponential stability by exploring the dissipative properties of the linear operator associated with the model through the Gearhart–Huang–Pruss theorem.
Applicable Analysis – Taylor & Francis
Published: Mar 23, 2024
Keywords: Thermoelastic system; thermodiffusion; functional partial differential equations; exponential stability; 35B35; 35R10; 35Q99
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