Well-Posedness of a Nonlinear Shallow Water Model for an Oscillating Water Column with Time-Dependent Air Pressure

We propose in this paper a new nonlinear mathematical model of an oscillating water column (OWC). The one-dimensional shallow equations the presence device are reformulated as transmission problem related to interaction between waves and fixed partially immersed structure. By imposing conservation total fluid-OWC energy non-damped scenario, we able derive condition that involves time-dependent air pressure inside chamber device, instead constant atmospheric Bocchi et al. (ESAIM Proc Surv 70:68–83, 2021). then show can be reduced quasilinear hyperbolic initial boundary value with semi-linear determined by ODE depending on trace solution PDE at boundary. Local well-posedness for general problems type is established via iterative scheme using linear estimates ODE.