Stabilization of a thermoelastic diffusion system of type II damped and delayed

ABSTRACT

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.

KEYWORDS:

• Thermoelastic system
• thermodiffusion
• functional partial differential equations
• exponential stability

AMS CLASSIFICATIONS:

• 35B35
• 35R10
• 35Q99

Acknowledgments

The authors are grateful to the referees for their helpful comments and valuable remarks that help to improve the paper.

Disclosure statement

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Additional information

Funding

The author Baowei Feng acknowledges the support from the Fundamental Research Funds for the Central Universities. Grant No JBK2304084.