关键词:  partial differential equations, abstract operator, symbol, laplace transform

Abstract: We summarize several relevant principles for the application of abstract operators in partial differential equations, and combine abstract operators with the Laplace transform. Thus we have developed the theory of partial differential equations of abstract operators and obtained the explicit solutions of initial value problems for a class of higher-order linear partial differential equations.

Key words:  partial differential equations, abstract operator, symbol, laplace transform