  We investigate models for nonlinear ultrasound propagation in soft biological
tissue based on the one that serves as the core for the software package
k-Wave. The systems are solved for the acoustic particle velocity, mass
density, and acoustic pressure and involve a fractional absorption operator. We
first consider a system that incorporates additional viscosity in the equation
for momentum conservation. By constructing a Galerkin approximation procedure,
we prove the local existence of its solutions. In view of inverse problems
arising from imaging tasks, the theory allows for the variable background mass
density, speed of sound, and the nonlinearity parameter in the systems.
Secondly, under stronger conditions on the data, we take the vanishing
viscosity limit of the problem, thereby rigorously establishing the existence
of solutions for the limiting system as well.
