Fundamental models in nonlinear acoustics part I. Analytical comparison

Abstract: This work is concerned with the study of fundamental models from nonlinear acoustics. In Part~I, a hierarchy of nonlinear damped wave equations arising in the description of sound propagation in thermoviscous fluids is deduced. In particular, a rigorous justification of two classical models, the Kuznetsov and Westervelt equations, retained as limiting systems for consistent initial data, is given. Numerical comparisons that confirm and complement the theoretical results are provided in Part~II.