Page 194 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 194
OPERATOR SEMIGROUPS AND EVOLUTION EQUATIONS (MS-29)
Embeddability of matrices into real and positive semigroups
Agnes Radl, radl@math.tu-berlin.de
TU Berlin, Germany
Coauthor: Tanja Eisner
It is a well-known problem whether a Markov matrix is embeddable into a Markov semigroup,
see the recent survey [1]. We consider a similar problem: Given a (finite or infinite) real/positive
matrix T , is it embeddable into a real/positive C0-semigroup, i. e., is there a real/positive semi-
group (T (t))t≥0 such that T (1) = T ? We will give necessary and sufficient conditions for
embeddability.
References
[1] M. Baake and J. Sumner, Notes on Markov embedding, Lineare Algebra Appl. 594 (2020).
Subclasses of Partial Contraction Mapping and generating evolution
system on Semigroup of Linear Operators
Kamilu Rauf, krauf@unilorin.edu.ng
University of Ilorin, Ilorin, Nigeria
Coauthor: Akinola Yussuff Akinyele
Some properties of C0-Semigroup are investigated and used to derive properties of ω-Order Pre-
serving and Reversing Partial Contraction Mapping where homogeneous, inhomogeneous and
regularity of mild solution for analytic semigroups are engaged. Furthermore, the subclasses
performed like semigroup of linear operators. Moreover, semigroup of linear operator generated
by ω-order reversing partial contraction mapping (ω-ORCPn) as the infinitesimal generator of
a C0-semigroup is discussed. It is an attempt to obtain results on evolution systems and stable
families of generators considering the homogeneous and inhomogeneous initial value problem.
Null-Controllability for Parabolic Equations
Christian Seifert, christian.seifert@tuhh.de
Technische Universität Hamburg, Germany
In this talk we study various notions of null-controllability of systems in Banach spaces. In an
abstract Banach space setting we show that an uncertainty relation together with a dissipation
estimate implies a so-called final state observability estimate with explicit dependence on the
model parameters. This estimate applied to the dual system in turn is in general equivalent to
an approximate notion of null-controllability, and in special cases also to null-controllability
of the original system. Our approach unifies and generalizes the respective advantages from
earlier results obtained in the context of Hilbert spaces. As an application we consider parabolic
equations induced by strongly elliptic operators on Lp spaces for 1 ≤ p < ∞.
The talk is based on joint work with Clemens Bombach, Dennis Gallaun and Martin Taut-
enhahn.
192
Embeddability of matrices into real and positive semigroups
Agnes Radl, radl@math.tu-berlin.de
TU Berlin, Germany
Coauthor: Tanja Eisner
It is a well-known problem whether a Markov matrix is embeddable into a Markov semigroup,
see the recent survey [1]. We consider a similar problem: Given a (finite or infinite) real/positive
matrix T , is it embeddable into a real/positive C0-semigroup, i. e., is there a real/positive semi-
group (T (t))t≥0 such that T (1) = T ? We will give necessary and sufficient conditions for
embeddability.
References
[1] M. Baake and J. Sumner, Notes on Markov embedding, Lineare Algebra Appl. 594 (2020).
Subclasses of Partial Contraction Mapping and generating evolution
system on Semigroup of Linear Operators
Kamilu Rauf, krauf@unilorin.edu.ng
University of Ilorin, Ilorin, Nigeria
Coauthor: Akinola Yussuff Akinyele
Some properties of C0-Semigroup are investigated and used to derive properties of ω-Order Pre-
serving and Reversing Partial Contraction Mapping where homogeneous, inhomogeneous and
regularity of mild solution for analytic semigroups are engaged. Furthermore, the subclasses
performed like semigroup of linear operators. Moreover, semigroup of linear operator generated
by ω-order reversing partial contraction mapping (ω-ORCPn) as the infinitesimal generator of
a C0-semigroup is discussed. It is an attempt to obtain results on evolution systems and stable
families of generators considering the homogeneous and inhomogeneous initial value problem.
Null-Controllability for Parabolic Equations
Christian Seifert, christian.seifert@tuhh.de
Technische Universität Hamburg, Germany
In this talk we study various notions of null-controllability of systems in Banach spaces. In an
abstract Banach space setting we show that an uncertainty relation together with a dissipation
estimate implies a so-called final state observability estimate with explicit dependence on the
model parameters. This estimate applied to the dual system in turn is in general equivalent to
an approximate notion of null-controllability, and in special cases also to null-controllability
of the original system. Our approach unifies and generalizes the respective advantages from
earlier results obtained in the context of Hilbert spaces. As an application we consider parabolic
equations induced by strongly elliptic operators on Lp spaces for 1 ≤ p < ∞.
The talk is based on joint work with Clemens Bombach, Dennis Gallaun and Martin Taut-
enhahn.
192
