Author(s) :
Robert Altmann
,
Christoph Zimmer
Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 07-2017
MSC 2000
- 35B65 Smoothness and regularity of solutions of PDE
-
35R10 Partial functional-differential or differential-difference equations, with or without deviating arguments
-
65Q05 Difference and functional equations, recurrence relations
Abstract :
We consider linear partial differential equations with an additional delay term, which - under spatial discretization - lead to ordinary differential equations with fixed delay of retarded type. This means that the semi-discrete solution gains smoothness over time. For the concept of classical, mild, and weak solutions we analyse whether this effect also takes place in the original system. We show that some systems behave in a neutral way only. As a result, the smoothness of the exact solution remains unchanged instead of gaining smoothness over time.
Keywords :
linear PDEs, delay differential equations, retarded, neutral, smoothing property