Well-posedness for the abstract Blackstock–Crighton–Westervelt equation

• Autor(a) principal: Gambera, Laura R. [UNESP]
• Data de Publicação: 2020
• Outros Autores: Lizama, Carlos, Prokopczyk, Andréa [UNESP]
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://dx.doi.org/10.1007/s00028-020-00580-3; http://hdl.handle.net/11449/198824
• topic: Blackstock–Crighton–Westervelt; Resolvent families; Well-posedness

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.