Global Existence and Uniqueness of Weak and Regular Solutions of Shallow Shells with Thermal Effects

Abstract

We study a dynamical thin shallow shell whose elastic deformations are described by a nonlinear system of Marguerre---Vlasov's type under the presence of thermal effects. Our main result is the proof of a global existence and uniqueness of a weak solution in the case of clamped boundary conditions. Standard techniques for uniqueness do not work directly in this case. We overcame this difficulty using recent work due to Lasiecka (Appl Anal 4:1376---1422, 1998).