Homogenization of high frequency nonlinear acoustics equations

Abstract

High frequency nonlinear acoustics equations proposed in [1] are considered. The acoustic characteristics of the medium rapidly oscillate. This model describes the propagation of pulses of sound shocks generated by supersonic planes, blast waves in atmosphere and ocean, continuous radiation of sound sources. An asymptotic solutions of high frequency nonlinear acoustics equations is constructed (when the characteristic size of inhomogeneity is small with respect to the height of the layer where the problem is posed

Keywords:

• High frequency non-linear acoustics
• stratified media
• homogenization
• eikonal equation
• transport equation
• estimates