Energy decay of variable-coefficient wave equation with acoustic boundary conditions and delay

ABSTRACT

In this paper, we consider a variable-coefficient wave equation with memory type acoustic boundary conditions and a constant time delay in the boundary feedback. Using the Riemannian geometry method, we prove the exponential decay of the system with memory type acoustic boundary conditions and a constant time delay under some suitable assumptions.

KEYWORDS:

• Wave equation
• variable-coefficients
• time delay
• memory type acoustic boundary
• exponential decay

AMS SUBJECT CLASSIFICATIONS:

• 35L20
• 35B35
• 93D20

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partially supported by NNSF of China [grant number 61374089]; NSF of Shanxi Province [2014011005-2]; Shanxi international science and technology cooperation projects [2014081026].