Global Existence of the Higher-Dimensional Linear System of Thermoviscoelasticity by Zhiyong Ma

“…We obtain a global existence result for the higher-dimensional thermoviscoelastic equations. Using semigroup approach, we will establish the global existence of homogeneous, nonhomogeneous, linear, semilinear, and nonlinear, thermoviscoelastic systems.…”
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Heat Equations Associated with Weinstein Operator and Applications by Hatem Mejjaoli

“…We establish a characterization for the homogeneous Weinstein-Besov spaces via the Weinstein heat semigroup. Next, we obtain the generalized Sobolev embedding theorems.…”
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Approximate Boundary Controllability for Semilinear Delay Differential Equations by Lianwen Wang

“…This paper considers the approximate controllability for a class of semilinear delay control systems described by a semigroup formulation with boundary control. Sufficient conditions for approximate controllability are established provided the approximate controllability of corresponding linear systems.…”
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Fixed points via a generalized local commutativity by Gerald F. Jungck

“…Let g:X→X. The concept of a semigroup of maps which is nearly commutative at g is introduced. …”
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The Relationship between Some Regular Subsemigroups of HypG2 by Weerapong Wongpinit, Sorasak Leeratanavalee

“…The concept of regular subsemigroups plays an important role in the theory of semigroup. In this work, we study the relationship between some regular subsemigroups on the monoid of all generalized hypersubstitutions of type τ=(2).…”
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Exponential Attractor for Lattice System of Nonlinear Boussinesq Equation by Min Zhao, Shengfan Zhou

“…We first verify the Lipschitz continuity of the continuous semigroup associated with the system. Then, we provide an estimation of the tail of the difference between two solutions of the system. …”
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Existence of Almost Periodic Solutions for Impulsive Neutral Functional Differential Equations by Junwei Liu, Chuanyi Zhang

“…Our results are based on Krasnoselskii’s fixed-point theorem combined with an exponentially stable strongly continuous operator semigroup. An example is given to illustrate the theory.…”
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Exponential Attractors for Parabolic Equations with Dynamic Boundary Conditions by Zhao-hui Fan

“…First, we give the existence of the exponential attractor in by proving that the corresponding semigroup satisfies the enhanced flattering property. …”
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Necessary Conditions for Optimality for Stochastic Evolution Equations by AbdulRahman Al-Hussein

“…We achieve our results through the semigroup approach.…”
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Quasilinear Stochastic Cauchy Problem in Abstract Colombeau Spaces by Irina V. Melnikova, Uljana A. Alekseeva

“…Generalized solutions to the abstract Cauchy problem for a quasilinear equation with the generator of an integrated semigroup and with terms reflecting nonlinear perturbations and white noise type perturbations are under consideration. …”
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New Concepts on Module Arens Regularity for Module Banach Algebras by Omid Pourbahri Rahpeyma, Davood Ebrahimi Bagha, Ghasem Soleimani Rad

“…Then a new module structure on the semigroup algebra l1S as l1ES-module with nontrivial right and left module actions is constructed. …”
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On the S-Invariance Property for S-Flows by Amin Saif, Adem Kılıçman

“…We define an equivalence relation on a topological space which is acted by topological monoid S as a transformation semigroup. Then, we give some results about the S-invariant classes for this relation. …”
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Ternary Weighted Function and Beurling Ternary Banach Algebra l1ω(S) by Mehdi Dehghanian, Mohammad Sadegh Modarres Mosadegh

“…Let S be a ternary semigroup. In this paper, we introduce our notation and prove some elementary properties of a ternary weight function ω on S. …”
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Controllability of semilinear stochastic delay evolution equations in Hilbert spaces by P. Balasubramaniam, J. P. Dauer

“…The controllability of semilinear stochastic delay evolution equations is studied by using a stochastic version of the well-known Banach fixed point theorem and semigroup theory. An application to stochastic partial differential equations is given.…”
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Optimal Control of Linear Impulsive Antiperiodic Boundary Value Problem on Infinite Dimensional Spaces by JinRong Wang, YanLong Yang

“…Using exponential stabilizability and discussing the impulsive evolution operators, without compactness and exponential stability of the semigroup governed by original principle operator, we present the existence of optimal controls. …”
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Exponential and Polynomial Decay Rates of a Porous Elastic System with Thermal Damping by Haiyan Li, Baowei Feng

“…By using the theory of the semigroup of the linear operator, the well-posedness is proven. …”
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Existence Theorems for Fractional Semilinear Integrodifferential Equations with Noninstantaneous Impulses and Delay by Bo Zhu, Minhui Zhu

“…In this paper, we consider a class of fractional semilinear integrodifferential equations with noninstantaneous impulses and delay. By the semigroup theory and fixed point theorems, we establish various theorems for the existence of mild solutions for the problem. …”
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Impulsive Fractional Semilinear Integrodifferential Equations with Nonlocal Conditions by Xue Wang, Bo Zhu

“…This paper is devoted to a class of impulsive fractional semilinear integrodifferential equations with nonlocal initial conditions. Based on the semigroup theory and some fixed point theorems, the existence theory of PC-mild solutions is established under the condition of compact resolvent operator. …”
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Nonlinear ergodic theorems for asymptotically almost nonexpansive curves in a Hilbert space by Gang Li, Jong Kyu Kim

“…We introduce the notion of asymptotically almost nonexpansive curves which include almost-orbits of commutative semigroups of asymptotically nonexpansive type mappings and study the asymptotic behavior and prove nonlinear ergodic theorems for such curves. …”
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Stability Analysis of the Periodic Solutions of Some Kinds of Predator-Prey Dynamical Systems by Neslihan Nesliye Pelen

“…To get the desired results, some aspects of semigroup theory for stability analysis and coincidence degree theory are used.…”
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