Alpha well-posedness,alpha stability,and the matrix theorems of H.-O. Kreiss

Summary For systems of partial differential equations with constant coefficients and for the corresponding difference equations the concepts of well-posedness and stability are introduced. These concepts are more general than strong well-posedness and stability on the one hand, and more restrictive than weak well-posedness (Petrovskii condition) and weak stability (von Neumann condition) on the other. Characterizations of these properties are established which partly extend the matrix theorems of H.-O. Kreiss. Also a Lax type theorem is valid in this setting.This author was supported by the Deutsche Forschungsgemeinschaft (Grant Go 261/4)