The talk Linear Heat Equation with Delay: Ill-Posedness vs. Well-Posedness
and Long-Time Behavior, by Michael Pokojovy, will be held on Monday October 12, 2015 at 9:00 in room K3.
We propose a Hilbert space solution theory for a nonhomogeneous heat equation with delay in the highest order derivatives with nonhomogeneous Dirichlet boundary conditions in a bounded domain. Under rather weak regularity assumptions on the data, we prove a well-posedness result and give an explicit representation of solutions. Further, we prove an exponential decay rate for the energy in the dissipative case. We also show that lower order regularizations lead to ill-posedness, also for higher-order equations. Finally, an application with physically relevant constants is given.