@article{Koonce2025, 
author = {Marvin Koonce and Jason Metcalfe},
title = {The sharp lifespan for a system of multiple speed wave equations: Radial case},
year = {2025},
journal = {Communications in Analysis and Mechanics},
volume = {17},
number = {3},
pages = {662-682},
keywords = {wave equations, local energy estimates, multiple speed, almost global existence},
url = {https://www.sciopen.com/article/10.3934/cam.2025026},
doi = {10.3934/cam.2025026},
abstract = {Ohta examined a system of multiple speed wave equations with small initial data and demonstrated a finite time blowup. We show, in the radial case, that the same system exists almost globally with the same lifespan as a lower bound. To do this, we use integrated local energy estimates,        r    p   weighted local energy estimates, the Morawetz estimate that results from using the scaling vector field as a multiplier, and mixed-speed ghost weights.}
}