Artículos de revistas
Well-posedness for the abstract Blackstock–Crighton–Westervelt equation
Journal of Evolution Equations.
Universidade Estadual Paulista (Unesp)
Universidad de Santiago de Chile
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.