Energy decay rate for the wave equation with variable coefficients and boundary source term

Abstract

In this paper, we consider the wave equation with variable coefficients and boundary source term. This work is devoted to prove the uniform energy decay rates of the wave equation with variable coefficients applying the Riemannian geometry method and modified multiplier method. This result gives us to classify the energy decay rate depending the growth near zero on the damping term.

COMMUNICATED BY:

• R. Magnanini

Keywords:

• Energy decay rate
• variable coefficients
• nonlinear source term
• Riemannian geometry

2000 Mathematics Subject Classifications:

• 35L05
• 35L20
• 35B35
• 35B40

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2019R1I1A3A01051714) and “Research Base Construction Fund Support Program” funded by Jeonbuk National University in 2019.