Strongly continuous semigroups on locally finite graphs

Abstract

In this paper, we propose a unified approach to prove the existence and uniqueness of the solutions of some of the evolution equations in combinatorial graphs. Our approach is based on the theory of strongly continuous semigroups in Banach spaces. Semigroups generated by heat, wave and Schrödinger equations are among the discussed equations. 

Key words: Graph, combinatorial Laplacian, evolution equation, C₀-semigroup.