On the influence of damping in hyperbolic equations with parabolic degeneracy

Abstract

This paper examines the effect of damping on a nonstrictly hyperbolic 2 × 2 2\times 2 system. It is shown that the growth of singularities is not restricted as in the strictly hyperbolic case where dissipation can be strong enough to preserve the smoothness of small solutions globally in time. Here, irrespective of the stabilizing properties of damping, solutions are found to break down in finite time on a line where two eigenvalues coincide in state space.