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This article concentrates on various operator semigroups arising in the study of viscous and incompressible flows. Of particular concern are the classical Stokes semigroup, the hydrostatic Stokes semigroup, the Oldroyd as well as the Ericksen-Leslie semigroup. Besides their intrinsic interest, the properties of these semigroups play an important role in the investigation of the associated nonlinear equations. This article is part of the theme issue 'Semigroup applications everywhere'.In this paper, we introduce a general framework to study linear first-order evolution equations on a Banach space X with dynamic boundary conditions, that is with boundary conditions containing time derivatives. Our method is based on the existence of an abstract Dirichlet operator and yields finally to equivalent systems of two simpler independent equations. In particular, we are led to an abstract Cauchy problem governed by an abstract Dirichlet-to-Neumann operator on the boundary space ∂X. Our approach is illustrated by several examples and various generalizations are indicated. selleck products This article is part of the theme issue 'Semigroup applications everywhere'.In this paper, we cross the boundary between semigroup theory and general infinite-dimensional systems to bridge the isolated research activities in the two areas. Indeed, we first give a chronological history of the development of the semigroup approach for control theory. Second, we use the feedback theory to prove the well-posedness of a class of dynamic boundary problems. Third, the obtained results are applied to the well-posedness of neutral equations with non-autonomous past. We will also see that the strong connection between semigroup and control theories lies in feedback theory, where different kinds of perturbations appear. This article is part of the theme issue 'Semigroup applications everywhere'.The classical and modern theorems on convergence, approximation and asymptotic stability of semigroups of operators are presented, and their applications to recent biological models are discussed. This article is part of the theme issue 'Semigroup applications everywhere'.Only in the last 15 years or so has the notion of semi-uniform stability, which lies between exponential stability and strong stability, become part of the asymptotic theory of C0-semigroups. It now lies at the very heart of modern semigroup theory. After briefly reviewing the notions of exponential and strong stability, we present an overview of some of the best known (and often optimal) abstract results on semi-uniform stability. We go on to indicate briefly how these results can be applied to obtain (sometimes optimal) rates of energy decay for certain damped second-order Cauchy problems. This article is part of the theme issue 'Semigroup applications everywhere'.The notion Perron-Frobenius theory usually refers to the interaction between three properties of operator semigroups positivity, spectrum and long-time behaviour. These interactions gives rise to a profound theory with plenty of applications. By a brief walk-through of the field and with many examples, we highlight two aspects of the subject, both related to the long-time behaviour of semigroups (i) The classical question how positivity of a semigroup can be used to prove convergence to an equilibrium as t → ∞. (ii) The more recent phenomenon that positivity itself sometimes occurs only for large t, while being absent for smaller times. This article is part of the theme issue 'Semigroup applications everywhere'.This paper presents a survey of maximal inequalities for stochastic convolutions in 2-smooth Banach spaces and their applications to stochastic evolution equations. This article is part of the theme issue 'Semigroup applications everywhere'.In this paper, we prove the global in time solvability of the continuous growth-fragmentation-coagulation equation with unbounded coagulation kernels, in spaces of functions having finite moments of sufficiently high order. The main tool is the recently established result on moment regularization of the linear growth-fragmentation semigroup that allows us to consider coagulation kernels whose growth for large clusters is controlled by how good the regularization is, in a similar manner to the case when the semigroup is analytic. This article is part of the theme issue 'Semigroup applications everywhere'.We present the operator semigroups approach to the first- and second-order dynamical systems taking place on metric graphs. We briefly survey the existing results and focus on the well-posedness of the problems with standard vertex conditions. Finally, we show two applications to biological models. This article is part of the theme issue 'Semigroup applications everywhere'.Despite calls in the literature, little is known about how dimensions of a social and task nature relate to each other in school and out-of-school learning environments. This study explored whether interpersonal and task dimensions of the youth sport environment, as perceived by young people, are related, and, if so, how they are related. We used data from 310 adolescent sport participants from eastern Canada (Mage = 14.69 ± 1.60 years; 54.8% girls). Participants completed comprehensive assessments of interpersonal dimensions of the sport environment and the characteristics of learning activities they do in practices. We used canonical correlation analysis to examine the multivariate shared relationship between the variable sets. The relationship was largely captured by the first three functions in the canonical model. The first two functions revealed areas of intersection between perceptions of interpersonal and practice-based activity factors in the form of supports and challenges for the learning and development process in sport. Accounting for the participants' age, the third function displayed characteristics consistent with recent descriptions of complex environments in youth sport. The findings suggest that adolescents' perceptions of interpersonal- and task-related features of sport are interdependent, and highlight the relevance of including variables assessing both factors in studies that attempt to characterize and understand learning environments in sport and other achievement domains. Findings also afford new insights into whether dimensions of a social and task nature are complementary, and inadequacies in one dimension can be attenuated by strengths in another or not.