A CLASS OF FULLY NONLINEAR 2X2 SYSTEMS OF PARTIAL-DIFFERENTIAL EQUATIONS

This paper is a study of certain fully nonlinear 2x2 systems oi partial differential equations in one space variable and lime. The nonlinearity contains a, term proportional to \partial derivative U/partial derivative x\ where U = U(x,t) epsilon R(2) is the unknown function and \.\ is the Euclidean norm on R(2); i.e.; a term homogeneous of degree. 1 in partial derivative U/partial derivative x and singular al the origin. Such equations are motivated by hypoplasticity. The paper introduces a notion of hyperbolicity for such equations and, in the hyperbolic case proves existence of solutions for two initial value problems admitting: similarity solutions: the Riemann problem and the scale-invariant problem. Uniqueness is addressed in a companion paper.