This project consists of two parts. The first part is concerned with linear and nonlinear mathematical problems in solid mechanics. Specifically, we shall study foundations problems in the elastostatic theory of thin and slender bodies, optimal control problems involving viscoelastic bodies, and stress concentration problems in finite strain and materially nonlinear thin elastic bodies and shells. The second part deals with the development of new perturbation techniques for weakly nonlinear wave propagation problems. Specifically we shall study problems for which the linearized hyperbolic equations do not split up into individual unidirectional modes, and cases where the linearized problem is unstable even though the nonlinear problem has stable solutions. We shall also extend multiple scale perturbation techniques to problems with more than two dependent variables (as in nonisentropic flow) and to higher space dimensions as in two-dimensional shallow water flow and acoustics.
