On necessary and sufficient conditions for strong hyperbolicity in systems with differential constraints

REULA, OSCAR; ABALOS, JULIO FERNANDO

Cambridge

Workshop; Structure preservation and general relativity; 2019

Issac Newton Institute for Mathematical Science

In many physical applications, due to the presence of constraints, the number of equations in the partial differential equation systems is larger than the number of unknowns, thus the standard Kreiss conditions can not be directly applied to check whether the system admits a well posed initial value formulation. In this work we show necessary and sufficient conditions such that there exists a reduced set of equations, of the same dimensionality as the set of unknowns, which satisfy Kreiss conditions and so are well defined and properly behaved evolution equations. We do that by decomposing the systems using the Kronecker decomposition of matrix pencils and, once the conditions are met, we look for specific families of reductions. We show the power of the theory in the densitized, pseudo-differential ADM equations.