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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Finite AG-groupoid with left identity and left zero by Qaiser Mushtaq, M. S. Kamran

“…It is a nonassociative algebraic structure midway between a groupoid and a commutative semigroup. In this note, we show that if G is a finite AG-groupoid with a left zero then, under certain conditions, G without the left zero element is a commutative group.…”
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Exponentially Convex Functions on Hypercomplex Systems by Buthinah A. Bin Dehaish

“…The definition of such functions is a natural generalization of that defined on semigroup.…”
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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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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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Large Time Behavior for Weak Solutions of the 3D Globally Modified Navier-Stokes Equations by Junbai Ren

“…With the aid of energy methods and auxiliary decay estimates together with Lp-Lq estimates of heat semigroup, we derive the optimal upper and lower decay estimates of the weak solutions for the globally modified Navier-Stokes equations as C1(1+t)-3/4≤uL2≤C2(1+t)-3/4,  t>1. …”
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Spectral Analysis for a Wave/Plate Transmission System by Chengqiang Wang

“…Our result reads as follows: the spectrum of the infinitesimal generator of the semigroup associated with the system in question consists merely of an infinite sequence of eigenvalues which are all located in the open left half of the complex plane; the sequence of eigenvalues has the imaginary axis and another vertical line to the left of the imaginary axis as its asymptote lines; the energy of the system under consideration decreases to zero as time goes to infinity.…”
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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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Dynamics of Stochastic Coral Reefs Model with Multiplicative Nonlinear Noise by Zaitang Huang

“…By support theorem and Hörmander theorem, the Markov semigroup corresponding to the solutions is to prove the Foguel alternative. …”
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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 Well-Posedness and Stability Analysis of a Computer Series System by Xing Qiao, Dan Ma, Fu Zheng, Guangtian Zhu

“…This study is devoted to discussing the unique existence of the solution and the stability of the studied system. In view of c0 semigroup theory, we prove the existence of a unique nonnegative solution of the system. …”
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Generalized roughness of three dimensional ( $$\in ,\in \vee q$$ ∈ , ∈ ∨ q )-fuzzy ideals in terms of set-valued homomorphism by Shahida Bashir, Rabia Mazhar, Nasreen Kausar, Saziye Yaman, Syed Suleman Ali, Muneeb Ul Hassan Afzal

“…Many results and theorems of rough fuzzy ideals have been extended from semigroup and semiring, to ternary semiring by introducing the definition of a rough fuzzy subset of ternary semiring. …”
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The zero dispersion limit for the Benjamin–Ono equation on the line by Gérard, Patrick

“…We also investigate the special case of an initial datum equal to the characteristic function of a finite interval, and prove the lack of semigroup property for this zero dispersion limit.…”
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Quasigeostrophic Equations for Fractional Powers of Infinitesimal Generators by Luciano Abadias, Pedro J. Miana

“…In this paper we treat the following partial differential equation, the quasigeostrophic equation: ∂/∂t+u·∇f=-σ-Aαf,  0≤α≤1, where (A,D(A)) is the infinitesimal generator of a convolution C0-semigroup of positive kernel on Lp(Rn), with 1≤p<∞. …”
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Commutator Theorems for Fractional Integral Operators on Weighted Morrey Spaces by Zhiheng Wang, Zengyan Si

“…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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Time-Delayed Feedback Control of a Hydraulic Model Governed by a Diffusive Wave System by Boumediène Chentouf, Nejib Smaoui

“…Thereafter, we invoke semigroup theory to substantiate that the closed-loop system has a unique solution in an energy space. …”
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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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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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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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Functional differential equations with infinite delay in Banach spaces by Jin Liang, Tijun Xiao

“…Moreover, we discuss the relation between the exponential asymptotic stability of the zero solution of nonlinear functional differential equation with infinite delay in a Banach space and the exponential stability of the solution semigroup of the corresponding linear equation, and find that the exponential stability problem of the zero solution for the nonlinear equation can be discussed only in the exponentially fading memory phase space.…”
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