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Preprint 07-2017

On the smoothing property of linear delay partial differential equations

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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

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