Well-posedness and exponential stability for the logarithmic Lamé system with a time delay

ABSTRACT

This paper is concerned with the initial-boundary value problem for a logarithmic Lamé system with a time delay in a bounded domain. We prove the well-posedness of the system by utilizing the semigroup theory. Then, we prove the existence of global solutions by using the well-depth method. In addition, we establish an exponential stability decay result under appropriate assumptions on the weight of the time delay and that of frictional damping.

KEYWORDS:

• Logarithmic Lamé system
• global existence
• exponential stability
• delay term

AMS SUBJECT CLASSIFICATIONS:

• 35B40
• 35L05
• 35L15
• 35L70

Disclosure statement

No potential conflict of interest was reported by the authors.

Data availability

No data were used to support this study.

Additional information

Funding

The authors are grateful to DUBAP (ZGEF.20.009) for research funds. The third and the fourth authors would like to thank King Fahd University of Petroleum and Minerals (KFUPM) for its continuous support. This work was funded by KFUPM under Project # SB201026.