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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On representation of solutions to the heat equation by Auscher, Pascal, Hou, Hedong

“…We propose a simple method to obtain semigroup representation of solutions to the heat equation using a local $L^2$ condition with prescribed growth and a boundedness condition within tempered distributions. …”
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A Note on Impulsive Fractional Evolution Equations with Nondense Domain by Zufeng Zhang, Bin Liu

“…Some errors in the existing paper concerned with nondensely defined fractional differential equations are pointed out, and correct formula of integral solutions is established by using integrated semigroup and some probability densities. Sufficient conditions for the existence are obtained by applying the Banach contraction mapping principle. …”
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On the Initial Value Problem of Stochastic Evolution Equations in Hilbert Spaces by Xuping Zhang, Yongxiang Li, Pengyu Chen

“…The present paper studies the initial value problem of stochastic evolution equations with compact semigroup in real separable Hilbert spaces. The existence of saturated mild solution and global mild solution is obtained under the situation that the nonlinear term satisfies some appropriate growth conditions. …”
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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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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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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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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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On the H.-Q. Li inequality on step-two Carnot groups by Zhang, Ye

“…In this note we show that the gradient estimate of the heat semigroup, or more precisely the H.-Q. Li inequality, is preserved under tensorization, some suitable group epimorphism, and central sum. …”
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Another special role of $ \mathrm{L}^\infty $-spaces-evolution equations and Lotz' theorem by Christian Budde

“…In this paper, we review the underappreciated theorem by Lotz that tells us that every strongly continuous operator semigroup on a Grothendieck space with the Dunford-Pettis property is automatically uniformly continuous. …”
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(λ,μ)-Fuzzy Version of Ideals, Interior Ideals, Quasi-Ideals, and Bi-Ideals by Yuming Feng, P. Corsini

“…We introduced (λ,μ)-fuzzy ideals, (λ,μ)-fuzzy interior ideals, (λ,μ)-fuzzy quasi-ideals, and (λ,μ)-fuzzy bi-ideals of an ordered semigroup and studied them. When λ=0 and μ=1, we meet the ordinary fuzzy ones. …”
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Asymptotic Stability of Fractional Stochastic Neutral Differential Equations with Infinite Delays by R. Sakthivel, P. Revathi, N. I. Mahmudov

“…A set of novel sufficient conditions are derived with the help of semigroup theory and fixed point technique for achieving the required result. …”
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Existence and Attractivity for Fractional Evolution Equations by Yong Zhou, Jia Wei He, Bashir Ahmad, Ahmed Alsaedi

“…We establish sufficient conditions for the global attractivity of mild solutions for the Cauchy problems in the case that semigroup is compact.…”
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Stability on coupling SIR epidemic model with vaccination by Helong Liu, Houbao Xu, Jingyuan Yu, Guangtian Zhu

“…We assume that the instantaneous death and infection rates depend on the age. Applying semigroup theory and so forth, we investigate the existence of equilibria. …”
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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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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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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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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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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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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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