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Next talk of the Seminar (14:30, Room Sousa Pinto)
23/04/2024: “On
the structure of the infinitesimal generators of semigroups with discrete
Lyapunov functionals”
Carlos Rocha (IST - Instituto
Superior Técnico, Lisboa)
Dynamical systems generated by scalar reaction-diffusion
equations enjoy special properties that lead to a very simple structure for
the semiflow. Among these properties, the
monotone behavior of the number of zeros of the solutions plays an
essential role. This discrete Lyapunov functional contains important
information on the spectral behavior of the linearization and leads to a
Morse-Smale description of the dynamical system.
Other systems, like the linear scalar delay
differential equations under monotone feedback conditions, possess similar
kinds of discrete Lyapunov functionals.
Here we discuss and characterize classes of linear
equations that generate semiflows which preserve
the order given by the discrete Lyapunov function.
This is based on a joint work
with Giorgio Fusco (arXiv 2306.10403).
Next talk of the Seminar (14:30, Zoom Meeting)
30/04/2024: “Infinite
products of operators”
Mário Bessa (CMUP & Universidade Aberta)
Our aim is to describe the
spectral properties of infinite products of operators using a dynamical
systems approach as a guideline. The continuous-time point of view of this
problem will also be addressed with an emphasis on applications to
differential equations. Furthermore, we will see that these topics can also
be seen as models for studying the dynamics of certain functional spaces
(Sobolev spaces).
Link: https://videoconf-colibri.zoom.us/j/98503287367?pwd=NWQ2OVFkem4yVGJKU2VRd3dIUU1Kdz09
ID: 985 0328 7367
Password: 863694
This Seminar is supported in part by the
Portuguese Foundation for Science and Technology (FCT - Fundação para a Ciência e a Tecnologia),
through CIDMA - Center for Research and Development in Mathematics and
Applications, within project UIDB/04106/2020
(https://doi.org/10.54499/UIDB/04106/2020).
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