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Abstract
Singular perturbations are considered for the initial value problem for a weakly nonlinear hyperbolic equation of the second order with a small positive parameter multiplying the second order time dericative term. Uniform asymptotic results are established on sets bounded in the time direction. The proof uses energy estimates which require some delicacy due to the dependence of the characteristics on the small parameter.
The problem includes that of a vibrating string in a highly viscous medium when appropriate scaling is made. Similar results for the linear case have been obtained previously by Zlamal and Hsiao and Weinacht.