Author(s) :
Anton Schiela
Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 03-2013
MSC 2000
- 35K15 Initial value problems for second-order, parabolic equations
-
49K20 Problems involving partial differential equations
Abstract :
We present a concise proof for existence and uniqueness of solutions of linear parabolic PDEs. It is based on an analysis of the corresponding differential operator and its adjoint in appropriate spaces and simple enough to be presented in the context of an introductory lecture on optimal control of PDEs. Our approach also clarifies some aspects in the structure of first order optimality conditions as illustrated at an example.
Keywords :
parabolic PDEs, optimal control, existence theory