ABSTRACT
Reaction-diffusion equations and interaction phenomena on ramified networks with Kirchhoff type connecting operators have been investigated recently by several authors, cf. [1-11]. In this paper we present a strong maximum principle and an a priori estimate for semilinear parabolic network equations with excitatoric Kirchhofflaws in the ramification nodes. The results presented here extend those of [3, Chap.2] and [6] and include the proofs of the Lemma and Theorem 2 in [6]. Existence results for semilinear parabolic network equations can be found in [3] and [7].
