From PDEs with Boundary Control to the Abstract State Equation with an Unbounded Input Operator: A Tutorial

摘要: This tutorial paper explains in detail how mathematical models of.dynmical systems described by linear partial difflrential equations (PDEs) with controls the boundary conditions can be generalized as abstract control and then latter lead to state an unbounded input operator. We start two simple examples: one-dimensional heat equation Neumann condition wave Dirichlet-Neumann condition. These examples will serve a motivation for more general setup system from which we eventually derive intend give comprehensive introduction theorists who are not experts infinite-dimensional theory but want read understand papers this field.