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Demicompactness Results for Strongly Continuous Semigroups, Generators and Resolvents
Mediterranean Journal of Mathematics, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Asrar Elleuch +2 more
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Periodic strongly continuous semigroups
Annali di Matematica Pura ed Applicata, 1977It is shown that three possible definitions of periodicity of a strongly continuous semigroup are equivalent. A complete characterization of periodicity is obtained in terms of the infinitesimal generator. An example is given to illustrate how the results tie in with the classical theory of periodic continuous functions.
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Maximal asymptotics of certain class of strongly continuous semigroups
2017 25th Mediterranean Conference on Control and Automation (MED), 2017We consider a class of first order linear differential equations given in infinite-dimensional space. We study asymptotic behavior of individual solutions in the context of stability. In particular, we are looking for the slowest decaying solution, that is maximal asymptotic. We present some new result on nonexistence of maximal asymptotics for certain
Piotr Polak, Grigory M. Sklyar
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Operator Multipliers Generating Strongly Continuous Semigroups
Semigroup Forum, 1997Let \(X\) be a Banach space. Given a family of (not necessarily bounded) operators on \(X\), \(\{A(s):s\in\mathbb{R}\}\). We can define an operator \(\mathcal A\) on \(C_0(\mathbb{R},X)\) by \[ ({\mathcal A})(s)= A(s)f(s)\quad\text{for}\quad f\in D({\mathcal A})\quad\text{and} \quad s\in\mathbb{R}, \] for a suitable definition of the domain \(D ...
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Heat treatment modelling using strongly continuous semigroups
Computers in Biology and Medicine, 2015In this paper, mathematical simulation of bioheat transfer phenomenon within the living tissue is studied using the thermal wave model. Three different sources that have therapeutic applications in laser surgery, cornea laser heating and cancer hyperthermia are used.
Alaeddin Malek, Ghasem Abbasi
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Invariant subsets of strongly continuous semigroups
Integral Equations and Operator Theory, 1984Let A be the generator of a strongly continuous semigroup \(\{\) P(t): \(t\geq 0\}\) of continuous linear operators defined on a Banach space X. Let C be a \(\|.\|\)-closed convex subset of X and suppose that for every x in D(A) there exists a sequence \((x_ n: n\in ({\mathbb{N}}))\) in D(A) with the following properties: \(\lim \| x-x_ n\| =\lim \| Ax-
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ON THE SPECTRAL CHARACTERIZATION OF A STRONGLY CONTINUOUS PERTURBED SEMIGROUP
Acta Mathematica Scientia, 1995Abstract In this paper, we get a sufficient condition to estimate the essential type of a strongly continuous semigroup in a Banach space, using this condition we prove that the essential type of the strongly continuous semigroup don't increase under the A – smoothing perturbation and establish the spectral mapping theorem for the asymptotic parts of
Haiyan Wang, Mingzhu Yang
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WEAK CONVERGENCE THEOREMS FOR STRONGLY CONTINUOUS SEMIGROUPS OF PSEUDOCONTRACTIONS
Acta Mathematica Vietnamica, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Strongly continuous semigroups on locally finite graphs
Quaestiones Mathematicae, 2018In this paper, we propose a unified approach to prove the existence and uniqueness of the solutions of some of the evolution equations in combinatorial graphs. Our approach is based on the theory of strongly continuous semigroups in Banach spaces. Semigroups generated by heat, wave and Schrödinger equations are among the discussed equations. Key words:
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