Resonances for a solvable model of ultrasound scattering by a cell membrane

We study the resonances for scattering of acoustic waves by cell membrane. Due to the fact that we deal with this phenomenon only, we use the simplest model of the membrane as a potential supported by a surface. The asymptotics of the Green’s function with the singularity at the surface is obtained. The influence of the surface curvature on the resonances is investigated. An application of the result to explanation of selective cancer cell membrane destruction in ultrasonic field is discussed.