Formation of singularities for a class of nonlinear, hyperbolically degenerate initial-boundary value problems

Abstract

We examine a class of initial-boundary value problems of vector-valued solutions defined over a bounded domain in R n. The presence of degeneracy in this class leads to loss of hyperbolicity at the null solution which gives rise to breakdown on the boundary of the domain when Dirichlet boundary conditions are imposed. Although the equations are set in an arbitrary number of spatial dimensions, it is possible to predict a maximal interval of existence for C 1-solutions in this setting. A simple application to one-dimensional elasticity is also shown.