Abstract
In this paper, we consider the Cauchy problem for quasi-linear wave equations with multiple propagation speeds in space dimensions n ≥ 3. The case when the nonlinearities depending on both the unknown functions and their derivatives are studied. Based on some Klainerman-Sideris type weighted estimates and space-time L 2 estimates, the lifespan for quasilinear multi-speeds wave equations of small amplitude solutions are presented.
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Yi, D., Yao, ZA. The lifespan for quasi-linear wave equations with multiple-speeds in space dimensions n ≥ 3. manuscripta math. 132, 343–364 (2010). https://doi.org/10.1007/s00229-010-0350-8
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DOI: https://doi.org/10.1007/s00229-010-0350-8