$L^2$-well-posedness for Hyperbolic Mixed Problems

Abstract

Strongly hyperbolic differential equations become L-well-posed mixed problems under suitable boundary conditions. A concept of uniform Lopatinski's condition, given by S. Agmon Q], gives a sufficient condition for L-well-posedness. Moreover, it is known that some types of mixed problems become L-well-posed, which do not satisfy uniform Lopatinski's condition (cf. [J2], Q3], [Jf]). On the other hand, in the case of constant coefficients and half-space, a necessary and sufficient condition for jL-well-posedness is given by R. Agemi & T. Shirota \Jf] by the words of uniform L-well-posedness for boundary value problems of ordinary differential equations with parameters. But it is not so concrete to clear the role of uniform Lopatinski's condition. This paper is a trial of more concrete characterizations of L-well-posedness for strongly hyperbolic mixed problems. We consider the problem