Hyperbolic-parabolic singular perturbations for scalar nonlinearities

Abstract

A hyperbolic-parabolic singular perturbation problem is considered for a nonlinear wave equation used a model for an extensible nonlinear string. An initial-boundary value problem is treated in which there is an initial layer at t = 0. It is proved that the solution of the reduced problem approximates the solution of the full problem uniformly on sets bounded in the time direction. The approximation is not uniform for the time derivatives unless initial layer correctors are added

Keywords:

• Hyperbolic-parabolic singular perturbations
• scalar nonlinearity
• nonlinear wave equations

AMS(MOS):

• 35B25
• 73C50
• 73D35
• 73K03
• 35L20
• 35K20
• 35L05