On the Analyticity for the Generalized Quadratic Derivative Complex Ginzburg-Landau Equation by Chunyan Huang

“…The strategy is to develop uniform and dyadic exponential decay estimates for the generalized Ginzburg-Landau semigroup e-a+it-Δα to overcome the derivative in the nonlinear term.…”
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Backward Stochastic Differential Equations Coupled with Value Function and Related Optimal Control Problems by Tao Hao, Juan Li

“…We get the related dynamic programming principle (DPP) with the help of the stochastic backward semigroup which was introduced by Peng in 1997. By making use of a new, more direct approach, we prove that our nonlocal Hamilton-Jacobi-Bellman (HJB) equation has a unique viscosity solution in the space of continuous functions of at most polynomial growth. …”
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Approximate Biprojectivity of ℓ1-Munn Banach Algebras by G. Zarei, A. Pourabbas, M. Rostami, A. Sahami

“…Finally, we apply our results to Rees semigroup algebras.…”
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Weighted Pseudo Almost-Periodic Functions and Applications to Semilinear Evolution Equations by Jun Zhang, Ti-Jun Xiao, Jin Liang

“…Moreover, we prove an existence theorem for the weighted pseudo almost-periodic mild solution to the semilinear evolution equation: x′(t)=Ax(t)+f(t,x(t)), t∈ℝ, where A is the infinitesimal generator of an exponentially stable C0-semigroup. An application is also given to illustrate the abstract existence theorem.…”
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The Structure of φ-Module Amenable Banach Algebras by Mahmood Lashkarizadeh Bami, Mohammad Valaei, Massoud Amini

“…As a consequence, we show that, if S is an inverse semigroup with finite set E of idempotents and l1S is a commutative Banach l1E-module, then l1S** is φ**-module amenable if and only if S is finite, when φ∈Homl1El1S is an epimorphism. …”
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A New Result of Stability for Thermoelastic-Bresse System of Second Sound Related with Forcing, Delay, and Past History Terms by Djamel Ouchenane, Zineb Khalili, Fares Yazid, Mohamed Abdalla, Bahri Belkacem Cherif, Ibrahim Mekawy

“…Under an appropriate assumption between the weight of the delay and the weight of the damping, we prove the well-posedness of the problem using the semigroup method, where an asymptotic stability result of global solution is obtained.…”
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Ulam-Hyers Stability of Trigonometric Functional Equation with Involution by Jaeyoung Chung, Chang-Kwon Choi, Jongjin Kim

“…Let S and G be a commutative semigroup and a commutative group, respectively, C and R+ the sets of complex numbers and nonnegative real numbers, respectively, and σ:S→S or σ:G→G an involution. …”
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Asymptotic stability of a repairable system with imperfect switching mechanism by Houbao Xu, Weihua Guo, Jingyuan Yu, Guangtian Zhu

“…We show that the system operator generates a positive C0-semigroup of contraction in a Banach space, therefore there exists a unique, nonnegative, and time-dependant solution. …”
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Compact Hermitian operators on projective tensor products of Banach algebras by T. K. Dutta, H. K. Nath, H. K. Sarmah

“…We prove that (i) every compact Hermitian operator T1 on U gives rise to a compact Hermitian operator T on U⊗pV having the properties that ‖T1‖=‖T‖ and sp(T1)=sp(T); (ii) if U and V are separable and U has Hermitian approximation property (HAP), then U⊗pV is also separable and has HAP; (iii) every compact analytic semigroup (CAS) on U induces the existence of a CAS on U⊗pV having some nice properties. …”
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Existence and Uniqueness of Mild Solutions to Impulsive Nonlocal Cauchy Problems by Mohamed Hannabou, Khalid Hilal, Ahmed Kajouni

“…By utilizing the theory of operators semigroup and fractional derivative, a new concept on a solution for our problem is introduced. …”
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Generalized Derivations on Prime Near Rings by Asma Ali, Howard E. Bell, Phool Miyan

“…The purpose of the present paper is to prove some theorems in the setting of a semigroup ideal of a 3-prime near ring admitting a generalized derivation, thereby extending some known results on derivations.…”
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Existence and optimal control of Hilfer fractional evolution equations by Zhou Mian, Zhou Yong, He Jia Wei, Liang Yong

“…The first part focuses on analyzing the existence and uniqueness of the mild solution using the fixed point theorem and semigroup theory. In the second part, an optimal control problem that admits an optimal pair is considered. …”
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The Order of Hypersubstitutions of Type (2,1) by Tawhat Changphas, Wonlop Hemvong

“…Therefore, it is interesting and useful to know how semigroup or monoid properties of monoids of hypersubstitutions transfer under this Galois connection to properties of the corresponding lattices of 𝑀-solid varieties. …”
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An Equivalence between the Limit Smoothness and the Rate of Convergence for a General Contraction Operator Family by Maxim J. Goldberg, Seonja Kim

“…For example, At is a diffusion semigroup (with T=0,∞). For W a finite measure space and w∈W, select real-valued hw∈L2X, defined everywhere, with hwL2X≤1. …”
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Boundedness of Lusin-area and gλ* functions on localized Morrey-Campanato spaces over doubling metric measure spaces by Haibo Lin, Eiichi Nakai, Dachun Yang

“…If χ has the volume regularity Property (P), the authors then establish the boundedness of the Lusin-area function, which is defined via kernels modeled on the semigroup generated by the Schrödinger operator, from ερa,p(χ) to ε̃ρa,p(χ) without invoking any regularity of considered kernels. …”
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Controllability of Mild Solution of Nonlocal Conformable Fractional Differential Equations by Mohamed Hannabou, Mohamed Bouaouid, Khalid Hilal

“…/dtα is the vectorial conformable fractional derivative of order α∈0,1 in a Banach space X and A is the infinitesimal generator of a semigroup Ttt≥0 on X. The element x0 is a fixed vector in X and f, g are given functions. …”
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Existence of Some Semilinear Nonlocal Functional Differential Equations of Neutral Type by Hsiang Liu, Cheng-Wen Liao, Chin-Tzong Pang

“…The linear part of the equations is assumed to generate a compact analytic semigroup of bounded linear operators, whereas the nonlinear part satisfies the Carathëodory condition and is bounded by some suitable functions. …”
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Controllability and Observability of Nonautonomous Riesz-Spectral Systems by Sutrima Sutrima, Christiana Rini Indrati, Lina Aryati

“…In this paper, we consider some relevant aspects regarding the controllability and observability for the nonautonomous Riesz-spectral systems including the Sturm-Liouville systems using a C0-quasi-semigroup approach. Three examples are provided. The first is related to sufficient conditions for the existence of solutions and the others are to confirm the approximate controllability and observability of the nonautonomous Riesz-spectral systems and Sturm-Liouville systems, respectively.…”
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Spatial and Temporal Dynamics of a Viral Infection Model with Two Nonlocal Effects by Xiaoyan Wang, Yuming Chen, Junyuan Yang

“…We propose and study a viral infection model with two nonlocal effects and a general incidence rate. First, the semigroup theory and the classical renewal process are adopted to compute the basic reproduction number R0 as the spectral radius of the next-generation operator. …”
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Asymptotically Almost Periodic Solutions for a Class of Stochastic Functional Differential Equations by Aimin Liu, Yongjian Liu, Qun Liu

“…The condition of being uniformly exponentially stable of the strongly continuous semigroup {Tt}t≥0 is essentially removed, which is generated by the linear densely defined operator A∶D(A)⊂L2(ℙ,ℍ)→L2(ℙ,ℍ), only using the exponential trichotomy of the system, which reflects a deeper analysis of the behavior of solutions of the system. …”
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