Ein stabiles Schichtenverfahren für allgemeine lineare Evolutionsgleichungen

Summary By generalizing Rothe's method of lines to initial value problemsu=A u, u(0)=u ₀ in Banach-spaces one obtains an approximation method that can be investigated within the theory of Lax and richtmyer 2]. It is well known that the generalized solutions of properly posed problems are semi-groups of class (C₀). In this paper the relation between the infinitesimal generator of that semi-group and the operatorA of the initial-value problem is discussed. As a consequence of the representation theorem of Hille-Yosida-Phillips one obtains that the method in question is stable iff the initial value problem is properly posed.

---

---

Die Arbeit ist die gekürzte Fassung eines Teils meiner Dissertation 7], die ich am Lehrstuhl von Prof. G. Hämmerlin anfertigte. Ihm danke ich herzlich für die Unterstützung bei der Anfertigung der Arbeit.