A rigorous derivation and energetics of a wave equation with fractional damping

Abstract We consider a linear system that consists of wave equation on horizontal hypersurface and parabolic in the half space below. The model describes longitudinal elastic waves organic monolayers at water–air interface, which is an experimental setup relevant for understanding propagation biological membranes. study scaling regime where length scale much larger than vertical provide rigorous limit leading to fractionally damped membrane. associated existence results via semigroup theory show convergence solutions limit. Moreover, based energy–dissipation structure full model, we derive natural energy dissipation function with time derivative order 3/2.