Well-posedness for the abstract Blackstock–Crighton–Westervelt equation - Gambera, Laura R. [UNESP]; Lizama, Carlos; Prokopczyk, Andréa [UNESP] (Springer Nature, 2020)
In this paper, an abstract degenerate hyperbolic equation is considered that includes the semilinear Blackstock–Crighton–Westervelt equation. By proposing a new approach based on strongly continuous semigroups and resolvent families of operators, we prove an explicit representation of the strong and mild solutions for the linearized model by means of a kind of variation of parameters formula. Moreover, we show that under nonlocal initial conditions, the existence of a mild solution of the semilinear equation can be established.
Keywords: Blackstock–Crighton–Westervelt; Resolvent families; Well-posedness