Fast energy decay for wave equations with variable damping coefficients in the 1-D half line

Abstract

We derive fast decay estimates of the total energy for wave equations with localized variable damping coefficients, which are dealt with in the one dimensional half line $(0,\infty)$. The variable damping coefficient vanishes near the boundary $x = 0$, and is effective critically near spatial infinity $x = \infty$.

Submitted in J. Math. Anal. Appl. (This version includes a little modification, which is not essential)