Tangential Differential Equations for Dynamical Thin/Shallow Shells

Abstract We present the mathematical construction of a dynamical second order operational differential equation for thin/shallow shells from elasticity by using the tangential differential calculus and the oriented boundary distance function. This model extends to thin/shallow shells the “natural theory” and the theory of Love–Kirchhoff of plates. We specify the appropriate function spaces, and give existence and uniqueness theorems.