Estimates for Unimodular Multipliers on Modulation Hardy Spaces by Jiecheng Chen, Dashan Fan, Lijing Sun, Chunjie Zhang

“…Finally, we investigate the boundedness of the operator eit|Δ|α/2 for α>0 and obtain the local well-posedness for the Cauchy problem of some nonlinear partial differential equations with fundamental semigroup eit|Δ|α/2.…”
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Complete positivity order and relative entropy decay by Li Gao, Marius Junge, Nicholas LaRacuente, Haojian Li

“…We prove that for a GNS-symmetric quantum Markov semigroup, the complete modified logarithmic Sobolev constant is bounded by the inverse of its complete positivity mixing time. …”
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Estimates for Multilinear Commutators of Generalized Fractional Integral Operators on Weighted Morrey Spaces by Sha He, Taotao Zheng, Xiangxing Tao

“…Let L be the infinitesimal generator of an analytic semigroup on L2(Rn) with Gaussian kernel bounds, and let L-α/2 be the fractional integrals of L for 0<α<n. …”
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Dichotomies with No Invariant Unstable Manifolds for Autonomous Equations by Răzvan O. Moşincat, Ciprian Preda, Petre Preda

“…We analyze the existence of (no past) exponential dichotomies for a well-posed autonomous differential equation (that generates a C0-semigroup {𝑇(𝑡)}𝑡≥0). The novelty of our approach consists in the fact that we do not assume the T(t)-invariance of the unstable manifolds. …”
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Global Analysis of a Discrete Nonlocal and Nonautonomous Fragmentation Dynamics Occurring in a Moving Process by E. F. Doungmo Goufo, S. C. Oukouomi Noutchie

“…Our system involving transport and nonautonomous fragmentation processes, where in addition, new particles are spatially randomly distributed according to some probabilistic law, is investigated by means of forward propagators associated with evolution semigroup theory and perturbation theory. The full generator is considered as a perturbation of the pure nonautonomous fragmentation operator. …”
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On the Complex Inversion Formula and Admissibility for a Class of Volterra Systems by Ahmed Fadili, Hamid Bounit

“…We first present results on the validity of the inverse formula of the Laplace transform for the resolvent families associated with scalar Volterra integral equations of convolution type in Banach spaces, which extends and improves the results in Hille and Philllips (1957) and Cioranescu and Lizama (2003, Lemma 5), respectively, including the stronger version for a class of scalar Volterra integrodifferential equations of convolution type on unconditional martingale differences UMD spaces, provided that the leading operator generates a C0-semigroup. Next, a necessary and sufficient condition for Lp-admissibility p∈1,∞ of the system's control operator is given in terms of the UMD-property of its underlying control space for a wider class of Volterra integrodifferential equations when the leading operator is not necessarily a generator, which provides a generalization of a result known to hold for the standard Cauchy problem (Bounit et al., 2010, Proposition 3.2).…”
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Immune response in virus model structured by cell infection-age by Cameron Browne

“…We characterize solutions to our system utilizing semigroup theory, determine equilibria and reproduction numbers, and prove stability and persistence results. …”
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Integrated Fractional Resolvent Operator Function and Fractional Abstract Cauchy Problem by Ya-Ning Li, Hong-Rui Sun

“…We firstly prove that β-times integrated α-resolvent operator function ((α,β)-ROF) satisfies a functional equation which extends that of β-times integrated semigroup and α-resolvent operator function. Secondly, for the inhomogeneous α-Cauchy problem cDtαu(t)=Au(t)+f(t), t∈(0,T), u(0)=x0, u'(0)=x1, if A is the generator of an (α,β)-ROF, we give the relation between the function v(t)=Sα,β(t)x0+(g1*Sα,β)(t)x1+(gα-1*Sα,β*f)(t) and mild solution and classical solution of it. …”
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The work of Glenn F. Webb by William E. Fitzgibbon

“…He is a Fellow of the American Mathematical Society.Glenn's scientific career chronicles an evolution of scientific workthat began with his interest in nonlinear semigroup theory and leads up tohis current activity in biomedical mathematics. …”
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Devaney Chaos and Distributional Chaos in the Solution of Certain Partial Differential Equations by Xavier Barrachina, J. Alberto Conejero

“…The notion of distributional chaos has been recently added to the study of the linear dynamics of operators and C0-semigroups of operators. We will study this notion of chaos for some examples of C0-semigroups that are already known to be Devaney chaotic.…”
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On quasi-ideals of semirings by Christoph Dönges

“…Corresponding results to those given here for semirings are mostly known as well for rings as for semigroups, but often proved by different methods. All proofs of our paper, however, apply simultaneously to semirings, rings and semigroups (cf. …”
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Local distributions of multiplicative functions by Rimantas Skrabutėnas

“… In the present paper the local distribution laws of values of multiplicative arithmetic functions g : G → R defined on arithmetical semigroups G and belonging to the class M(G) is considered. …”
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Navier-Stokes Equations with Potentials by Adriana-Ioana Lefter

“…Using the theory of nonlinear semigroups, we prove existence results for strong and weak solutions. …”
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Regularity of Global Attractor for the Reaction-Diffusion Equation by Hong Luo

“…By using an iteration procedure, regularity estimates for the linear semigroups, and a classical existence theorem of global attractor, we prove that the reaction-diffusion equation possesses a global attractor in Sobolev space Hk for all k>0, which attracts any bounded subset of Hk(Ω) in the Hk-norm.…”
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On Pure Hyperradical in Semihypergroups by Kostaq Hila, Krisanthi Naka

“…This paper deals with a class of algebraic hyperstructures called semihypergroups, which are a generalization of semigroups. In this paper, we introduce pure hyperradical of a hyperideal in a semihypergroup with zero element. …”
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On the boundedness of operators in LP(ιq) and Triebel-Lizorkin Spaces by João Pedro Boto

“…Applications are given to linear parabolic equations and to Schrödinger semigroups.…”
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The Hautus-Type Inequality for Abstract Fractional Cauchy Problems and Its Observability by Li Chen-Yu

“…In this paper, we investigate the observability of the fractional resolvent family, and we prove two main results: the first result shows a generalization of the Hautus-type test for observable exponentially stable semigroups to the fractional resolvent family and the second result shows the equivalence of the observability and the below boundedness of the linear operator on the wave packet when the generator conforms to a specific form.…”
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Exponential dichotomy for evolution families on the real line by Adina Luminiţa Sasu

“…As applications we obtain characterizations for uniform exponential dichotomy of semigroups.…”
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Existence of Global Solutions for Nonlinear Magnetohydrodynamics with Finite Larmor Radius Corrections by Fariha Elsrrawi, Harumi Hattori

“…Our techniques of proof are based on the existence of local solution by semigroups theory and a priori estimate.…”
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Some Indices over a New Algebraic Graph by Nurten Urlu Özalan

“…In this paper, we first introduce a new graph ΓN over an extension N of semigroups and after that we study and characterize the spectral properties such as the diameter, girth, maximum and minimum degrees, domination number, chromatic number, clique number, degree sequence, irregularity index, and also perfectness for ΓN. …”
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