The Principle of Limiting Amplitude for Symmetric Hyperbolic Systems in an Exterior Domain
Kiyoshi Mochizuki · Publications of the Research Institute for Mathematical Sciences · 1969
dxj > u(x, 0) = UQ(X) for x^G u(z, t)^N(z) for t>0, Here //, (^0) is a real number, i = \/^l, u(x, t) and g(x) are vector valued functions whose values lie in Cm, and M(x) (measurable), Aj(x) (smooth) and B(x) (continuous) are mxm matrix valued, bounded functions. The boundary space N(z) is a linear subspace of Cm of constant dimension which is smoothly varying on 9G. Our aim is to derive the limiting amplitude principle ; that is, we shall obtain the asymptotic behavior of solutions of the above problem. The assumptions which we require below are summarized as ( I ) M(x) is positive definite. L = — \^ A Ax) — 4- B(x)] is formally