Gravitational corner conditions in holography by Gary T. Horowitz, Diandian Wang

“…Abstract Contrary to popular belief, asymptotically anti-de Sitter solutions of gravitational theories cannot be obtained by taking initial data (satisfying the constraints) on a spacelike surface, and choosing an arbitrary conformal metric on the timelike boundary at infinity. There are an infinite number of corner conditions that also must be satisfied where the initial data surface hits the boundary. …”
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Granular media equation with double-well external landscape: limiting steady state by Tugaut, Julian

“…In this paper, we give a simple condition on the initial state of the granular media equation which ensures that the limit as the time goes to infinity is the unique steady state with positive center of mass. …”
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Center problem for quartic differential systems with an affine invariant straight line of maximal multiplicity by Olga Vacaraș

“…In this paper the quartic differential systems with a center-focus critical point and non-degenerate infinity are examined. We show that in this family the maximal multiplicity of an affine invariant straight line is six. …”
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Asymptotic behaviour of solutions for porous medium equation with periodic absorption by Yin Jingxue, Wang Yifu

“…In contrast to the equation without sources, we show that the solutions may not decay but may be attracted into any small neighborhood of the set of all nontrivial periodic solutions, as time tends to infinity. As a direct consequence, the null periodic solution is unstable. …”
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Existence of Homoclinic Orbits for a Class of Asymptotically p-Linear Difference Systems with p-Laplacian by Qiongfen Zhang, X. H. Tang

“…By applying a variant version of Mountain Pass Theorem in critical point theory, we prove the existence of homoclinic solutions for the following asymptotically p-linear difference system with p-Laplacian Δ(|Δu(n-1)|p-2Δu(n-1))+∇[-K(n,u(n))+W(n,u(n))]=0, where p∈(1,+∞), n∈ℤ, u∈ℝN, K,W:ℤ×ℝN→ℝ are not periodic in n, and W is asymptotically p-linear at infinity.…”
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Large Time Behavior of the Vlasov-Poisson-Boltzmann System by Li Li, Shuilin Jin, Li Yang

“…To be precise, we prove that when time goes to infinity, the solution of VPB system tends to global Maxwellian state in a rate Ot−∞, by using a method developed for Boltzmann equation without force in the work of Desvillettes and Villani (2005). …”
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Entropy numbers of embeddings of function spaces with Muckenhoupt weights, III. Some limiting cases by Dorothee D. Haroske, Leszek Skrzypczak

“…This extends our previous results [25] to more general weights of logarithmically disturbed polynomial growth, both near some singular point and at infinity. We obtain sharp asymptotic estimates for the entropy numbers of this embedding. …”
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Weak cosmic censorship, trapped surfaces, and naked singularities for the Einstein vacuum equations by Shlapentokh-Rothman, Yakov

“…The weak cosmic censorship conjecture posits that, generically, all singularities in General Relativity arising from regular asymptotically flat initial data should have a complete future null infinity. While this conjecture remains wide open, it has inspired many mathematical works concerning topics such as trapped surface formation and the construction of naked singularities. …”
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A Note on the Newman-Unti Group and the BMS Charge Algebra in Terms of Newman-Penrose Coefficients by Glenn Barnich, Pierre-Henry Lambert

“…The symmetry algebra of asymptotically flat spacetimes at null infinity in four dimensions in the sense of Newman and Unti is revisited. …”
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Universal Verma Modules and the Misra-Miwa Fock Space by Arun Ram, Peter Tingley

“…Partitions also index the polynomial Weyl modules for Uq(glN) as N tends to infinity. We explain how the powers of v which appear in the Misra-Miwa Fock space also appear naturally in the context of Weyl modules. …”
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A curious property of series involving terms of generalized sequences by Odoardo Brugia, Piero Filipponi

“…The aim of this paper is to find triples (p,q,r) for which the series Un  (p,q)/rn and Vn  (p,q)/rn (for r running from 0 to infinity) are unconcerned at the introduction of the factor n. …”
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On Unique Continuation for Navier-Stokes Equations by Zhiwen Duan, Shuxia Han, Peipei Sun

“…We take advantage of rotation transformation of the Navier-Stokes equations to prove the “logarithmic convexity” of certain quantities, which measure the suitable Gaussian decay at infinity to obtain the Gaussian decay weighted estimates, as well as Carleman inequality. …”
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Modified Function Projective Synchronization for a Partially Linear and Fractional-Order Financial Chaotic System with Uncertain Parameters by Yehong Yang, Guohua Cao

“…Using the controller, the error systems converged to zero as time tends to infinity, and the uncertain parameters were also estimated so that the phenomenon of parameter distortion was effectively avoided. …”
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The Third Five-Parametric Hypergeometric Quantum-Mechanical Potential by T. A. Ishkhanyan, A. M. Ishkhanyan

“…Depending on an involved parameter, the potential presents either a short-range singular well (which behaves as inverse square root at the origin and vanishes exponentially at infinity) or a smooth asymmetric step-barrier (with variable height and steepness). …”
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Global Existence to an Attraction-Repulsion Chemotaxis Model with Fast Diffusion and Nonlinear Source by Yingjie Zhu, Fuzhong Cong

“…Moreover, we notice that the cell density goes to the maximum value when the diffusion coefficient of the cell density tends to infinity.…”
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Positive Solutions for a Nonhomogeneous Kirchhoff Equation with the Asymptotical Nonlinearity in R3 by Ling Ding, Lin Li, Jin-Ling Zhang

“…We study the following nonhomogeneous Kirchhoff equation: -(a+b∫R3‍|∇u|2dx)Δu+u=k(x)f(u)+h(x),  x∈R3,  u∈H1(R3),  u>0,  x∈R3, where f is asymptotically linear with respect to t at infinity. Under appropriate assumptions on k,f, and h, existence of two positive solutions is proved by using the Ekeland's variational principle and the Mountain Pass Theorem in critical point theory.…”
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Breather Positons and Rogue Waves for the Nonlocal Fokas-Lenells Equation by Chun Wang, Rong Fan, Zhao Zhang, Biao Li

“…In this nonlocal optical system, rogue waves can be generated when periods of breather positons go to infinity. In addition, we find two very interesting phenomena: one is that rogue waves sitting on a periodic line wave background are derived; the other is that a hybrid of rogue waves and a periodic kink wave is also constructed. …”
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On-Line Selection of c-Alternating Subsequences from a Random Sample by Robert W. Chen, Larry A. Shepp, Justín Ju-Chen Yang

“…We also give the optimal selection rate when the sample size goes to infinity.…”
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Dynamic Proportional Reinsurance and Approximations for Ruin Probabilities in the Two-Dimensional Compound Poisson Risk Model by Yan Li, Guoxin Liu

“…In addition, we obtain the Lundberg bounds and the Cramér-Lundberg approximation for the ruin probability and show that as the capital tends to infinity, the optimal strategies converge to the asymptotically optimal constant strategies. …”
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Strauss’s Radial Compactness and Nonlinear Elliptic Equation Involving a Variable Critical Exponent by Masato Hashizume, Megumi Sano

“…We point out that the decaying speed of q(x) at infinity plays an essential role on the compactness. …”
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