A Variational Approach to Boundary Value Problems for a Class of Nonlinear Systems of Mixed Type

Abstract

Transonic small disturbance theory in two dimensions leads to a nonlinear first-order system of mixed type. For such systems corresponding variational problems are formulated. These minimum problems are studied on closed sets of admissible functions satisfying certain boundedness constraints and entropy conditions. Existence theorems can be proved though the functionals need not be convex and the given sets are not compact. Furthermore, some properties of minimizers are derived.