Well-posedness for the abstract Blackstock–Crighton–Westervelt equation
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Gambera, Laura R. [UNESP]
Prokopczyk, Andréa [UNESP]
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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.
Blackstock–Crighton–Westervelt, Resolvent families, Well-posedness
Journal of Evolution Equations.