| Affiliation: | Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China -- and -- Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-72076, Tübingen, Germany ; Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China -- and -- Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-72076, Tübingen, Germany |
| Abstract: | In this paper, we exhibit a unified treatment of the mixed initial boundary value problem for second order (in time) parabolic linear differential equations in Banach spaces, whose boundary conditions are of a dynamical nature. Results regarding existence, uniqueness, continuous dependence (on initial data) and regularity of classical and strict solutions are established. Moreover, several examples are given as samples for possible applications. |
