Well-posedness and exponential decay of solutions for the Blackstock–Crighton–Kuznetsov equation

Abstract

The present work provides well-posedness and exponential decay results for the Blackstock–Crighton–Kuznetsov equation arising in the modeling of nonlinear acoustic wave propagation in thermally relaxing viscous fluids. First, we treat the associated linear equation by means of operator semigroups. Moreover, we derive energy estimates which we will use in a fixed-point argument in order to obtain well-posedness of the Blackstock–Crighton–Kuznetsov equation. Using a classical barrier argument we prove exponential decay of solutions.