Chaired by: prof. Piotr Zgliczyński, dr hab. Anna Ochal

Room: 1016

Date: Tuesday 12:15-13:45

Linear autonomous Retarded Functional Differential Equations (RFDEs)

TEMAT:   Linear autonomous Retarded Functional Differential Equations (RFDEs)

Opis:    I will present some theory of linear autonomous RFDEs (i.e. DEs
of the form $x'(t) = Ax_t$, where A is a linear operator and $x_t(s) = x(t+s), s in [-d, 0]$ is the so-called segment of the solution). We want to use the language of semidynamical systems and since the domain of A is infinite dimensional while its range is finite, one gets some special decomposition of the semigroup and the state space, useful for studying nonlinear systems later. The goal is to show spectral properties of the semigroup and discuss (non)existence of small solutions (nontrivial solutions that tend to 0 faster than any exponent).

Based on the book "Delay Equations: Functional-, Complex-, and Nonlinear Analysis" by O. Diekmann et al. (1994), Chapters 2-5

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