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Interpolating a Heat Conduction Problem and a Viscoelastic Problem

March 25 @ 2:00 pm - 3:00 pm

In this talk, we consider a generalization of the well-known telegraph problem to the fractional case in presence of a viscoelastic term. We first discuss the well-posedness of the system using a family of resolvent operators. Next, the stability of the system is addressed. Some light is shed on the roles of lower-order fractional derivatives as well as viscoelastic terms. It will be shown that only one of these two types of terms is enough to drive the system to equilibrium. The rate of stability is determined to be of Mittag-Leffler kind. Some smallness conditions on the relaxation function are needed in case of viscoelasticity. The results rely heavily on some proved properties of fractional derivatives and some newly introduced functionals. The main difficulties, due to the invalidity of some well-known properties in the integer-order case, will be highlighted.

Details

Date:
March 25
Time:
2:00 pm - 3:00 pm

Organizer

The Mathematics and Applications Colloquium (MAC)

Venue

Virtual