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Journal articles on the topic 'Non-asymptotic analysis'

Author: Grafiati

Published: 9 November 2024

Last updated: 7 July 2025

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1

Kaslovsky, Daniel N., and François G. Meyer. "Non-asymptotic analysis of tangent space perturbation." Information and Inference: A Journal of the IMA 3, no. 2 (2014): 134–87. http://dx.doi.org/10.1093/imaiai/iau004.

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2

Logemann, H., and E. P. Ryan. "Non-autonomous systems: asymptotic behaviour and weak invariance principles." Journal of Differential Equations 189, no. 2 (2003): 440–60. http://dx.doi.org/10.1016/s0022-0396(02)00144-4.

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3

Djafari Rouhani, Behzad. "Asymptotic properties of some non-autonomous systems in Banach spaces." Journal of Differential Equations 229, no. 2 (2006): 412–25. http://dx.doi.org/10.1016/j.jde.2006.07.010.

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4

Pileckas, Konstantin, and Alicija Raciene. "Non-stationary Navier–Stokes equations in 2D power cusp domain." Advances in Nonlinear Analysis 10, no. 1 (2021): 1011–38. http://dx.doi.org/10.1515/anona-2020-0165.

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Abstract The initial boundary value problem for the non-stationary Navier-Stokes equations is studied in 2D bounded domain with a power cusp singular point O on the boundary. We consider the case where the boundary value has a nonzero flux over the boundary. In this case there is a source/sink in O and the solution necessary has infinite energy integral. In the first part of the paper the formal asymptotic expansion of the solution near the singular point was constructed. In this, second part, the constructed asymptotic decomposition is justified, i.e., existence of the solution which is represented as the sum of the constructed asymptotic expansion and a term with finite energy norm is proved. Moreover, it is proved that the solution represented in this form is unique.

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5

da Silva, C. R. C., and B. Choi. "Non-asymptotic performance analysis of single-cycle detectors." IEEE Transactions on Wireless Communications 7, no. 10 (2008): 3732–37. http://dx.doi.org/10.1109/t-wc.2008.070639.

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6

Shah, Devavrat, Qiaomin Xie, and Zhi Xu. "Non-Asymptotic Analysis of Monte Carlo Tree Search." ACM SIGMETRICS Performance Evaluation Review 48, no. 1 (2020): 31–32. http://dx.doi.org/10.1145/3410048.3410066.

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7

Zuo, Yijun. "Non-asymptotic robustness analysis of regression depth median." Journal of Multivariate Analysis 199 (January 2024): 105247. http://dx.doi.org/10.1016/j.jmva.2023.105247.

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8

Schlier, Ch. "Discrepancy behaviour in the non-asymptotic regime." Applied Numerical Mathematics 50, no. 2 (2004): 227–38. http://dx.doi.org/10.1016/j.apnum.2003.12.004.

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9

Onitsuka, Masakazu. "Non-uniform asymptotic stability for the damped linear oscillator." Nonlinear Analysis: Theory, Methods & Applications 72, no. 3-4 (2010): 1266–74. http://dx.doi.org/10.1016/j.na.2009.08.010.

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10

Majd, Abderrazzak. "On the Asymptotic Analys of a Non-Symmetric Bar." ESAIM: Mathematical Modelling and Numerical Analysis 34, no. 5 (2000): 1069–85. http://dx.doi.org/10.1051/m2an:2000116.

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11

Pileckas, Konstantin, and Alicija Raciene. "Non-stationary Navier–Stokes equations in 2D power cusp domain." Advances in Nonlinear Analysis 10, no. 1 (2021): 982–1010. http://dx.doi.org/10.1515/anona-2020-0164.

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Abstract The initial boundary value problem for the non-stationary Navier-Stokes equations is studied in 2D bounded domain with a power cusp singular point O on the boundary. The case of the boundary value with a nonzero flow rate is considered. In this case there is a source/sink in O and the solution necessary has infinite energy integral. In the first part of the paper the formal asymptotic expansion of the solution near the singular point is constructed. The justification of the asymptotic expansion and the existence of a solution are proved in the second part of the paper.

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12

Attouch, Hedy, and Marc-Olivier Czarnecki. "Asymptotic Control and Stabilization of Nonlinear Oscillators with Non-isolated Equilibria." Journal of Differential Equations 179, no. 1 (2002): 278–310. http://dx.doi.org/10.1006/jdeq.2001.4034.

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13

Teles, Ricardo de Sa. "Pullback attractors for non-autonomous Bresse systems." Electronic Journal of Differential Equations 2022, no. 01-87 (2022): 05. http://dx.doi.org/10.58997/ejde.2022.05.

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This article concerns the asymptotic behavior of solutions of non-autonomous Bresse systems. We establish the existence of pullback attractor and upper semicontinuity of attractors as a non-autonomous perturbations tend to zero. In addition we study the continuity of attractors with respect to a parameter in a residual dense set.

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14

Poulimenos, A. G., and S. D. Fassois. "Asymptotic Analysis of Non-stationary Functional Series TARMA Estimators." IFAC Proceedings Volumes 42, no. 10 (2009): 1451–56. http://dx.doi.org/10.3182/20090706-3-fr-2004.00242.

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15

Lebon, F., R. Rizzoni, and S. Ronel-Idrissi. "Asymptotic analysis of some non-linear soft thin layers." Computers & Structures 82, no. 23-26 (2004): 1929–38. http://dx.doi.org/10.1016/j.compstruc.2004.03.074.

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16

EL-GEBEILY, MOHAMED, and KAMAL A. F. MOUSTAFA. "Asymptotic analysis of almost periodic weakly non-linear systems." International Journal of Control 54, no. 3 (1991): 561–75. http://dx.doi.org/10.1080/00207179108934176.

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17

Bai, X. S., and K. Seshadri. "Rate-ratio asymptotic analysis of non-premixed methane flames." Combustion Theory and Modelling 3, no. 1 (1999): 51–75. http://dx.doi.org/10.1088/1364-7830/3/1/004.

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18

Dickey, David A., Graciela González-Farías, and Nelson Muriel. "Asymptotic analysis of non-periodical cointegration with high seasonals." Boletín de la Sociedad Matemática Mexicana 25, no. 2 (2018): 443–59. http://dx.doi.org/10.1007/s40590-018-0201-2.

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19

Malyutina, T. I. "SOME ESTIMATES OF SPECIAL CLASSES OF INTEGRALS." Mathematical Modelling and Analysis 5, no. 1 (2000): 127–32. http://dx.doi.org/10.3846/13926292.2000.9637135.

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We study the integrals fb a f(t) exp(i| ln rt|σ) dt and obtain asymptotic formula for these functions of non‐regular growth. This is a peculiar kind of the theory asymptotic expansions. In particular, we get asymptotic formulae for different entire functions of non‐regular growth. Asymptotic formulas for Levin‐Pfluger entire functions of completely regular growth are well‐known [1]. Our formulas allow to find limiting Azarin's [2] sets for some subharmonic functions. The kernel exp(i| ln rt|σ) contains arbitrary parameter σ > 0. The integrals for σ ∈(0, 1), σ = 1, σ > 1 essentially differ. Our arguments can apply to more general kernels. We give a new variant of the classic lemma of Riemann and Lebesgue from the theory of the transformation of Fourier.

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20

Wang, Bixiang. "Asymptotic behavior of non-autonomous fractional stochastic reaction–diffusion equations." Nonlinear Analysis 158 (July 2017): 60–82. http://dx.doi.org/10.1016/j.na.2017.04.006.

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21

Miyazaki, Yoichi. "Asymptotic behavior of spectral functions for elliptic operators with non-smooth coefficients." Journal of Functional Analysis 214, no. 1 (2004): 132–54. http://dx.doi.org/10.1016/j.jfa.2003.12.003.

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22

Wu, Hao, Liming Wang, Xiaodong Wang, and Xiaohu You. "Asymptotic and Non-Asymptotic Analysis of Uplink Sum Rate for Relay-Assisted MIMO Cellular Systems." IEEE Transactions on Signal Processing 62, no. 6 (2014): 1348–60. http://dx.doi.org/10.1109/tsp.2013.2274642.

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23

Hayashi, Masahito, and Yuuya Yoshida. "Asymptotic and non-asymptotic analysis for a hidden Markovian process with a quantum hidden system." Journal of Physics A: Mathematical and Theoretical 51, no. 33 (2018): 335304. http://dx.doi.org/10.1088/1751-8121/aacde9.

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24

Werner, Wendelin. "Asymptotic behaviour of disconnection and non-intersection exponents." Probability Theory and Related Fields 108, no. 1 (1997): 131–52. http://dx.doi.org/10.1007/s004400050104.

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25

Jung, Chang-Yeol, and Roger Temam. "Singularly perturbed problems with a turning point: The non-compatible case." Analysis and Applications 12, no. 03 (2014): 293–321. http://dx.doi.org/10.1142/s0219530513500279.

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The singularly perturbed problems with a turning point were discussed in [21]. The case where the limit problem is compatible with the given data was fully resolved. However, with limited compatibility conditions on the data, the asymptotic expansions were constructed only up to the order of the level of compatibilities. In this paper, using a smooth cut-off function compactly supported around the turning point we resolve the difficulties incurred from the non-compatible data and finally provide the full asymptotic expansions up to any order.

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26

Heim, Bernhard, and Markus Neuhauser. "Asymptotic distribution of the zeros of recursively defined non-orthogonal polynomials." Journal of Approximation Theory 275 (March 2022): 105700. http://dx.doi.org/10.1016/j.jat.2022.105700.

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27

Karagulyan, A. G. "Non-Asymptotic Guarantees for Sampling by Stochastic Gradient Descent." Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences) 54, no. 2 (2019): 71–78. http://dx.doi.org/10.3103/s1068362319020031.

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28

Deng, Chang-Song, and René L. Schilling. "Exact asymptotic formulas for the heat kernels of space and time-fractional equations." Fractional Calculus and Applied Analysis 22, no. 4 (2019): 968–89. http://dx.doi.org/10.1515/fca-2019-0052.

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Abstract This paper aims to study the asymptotic behaviour of the fundamental solutions (heat kernels) of non-local (partial and pseudo differential) equations with fractional operators in time and space. In particular, we obtain exact asymptotic formulas for the heat kernels of time-changed Brownian motions and Cauchy processes. As an application, we obtain exact asymptotic formulas for the fundamental solutions to the n-dimensional fractional heat equations in both time and space $$\begin{array}{} \displaystyle \frac{\partial^\beta}{\partial t^\beta}u(t,x) = -(-\Delta_x)^\gamma u(t,x), \quad \beta,\gamma\in(0,1). \end{array}$$

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29

Czarnecki, Marc-Olivier. "Asymptotic control and stabilization of nonlinear oscillators with non isolated equilibria, a note: from L1 to non L1." Journal of Differential Equations 217, no. 2 (2005): 501–11. http://dx.doi.org/10.1016/j.jde.2005.06.026.

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30

Vorotnikov, Dmitry. "Asymptotic behavior of the non-autonomous 3D Navier–Stokes problem with coercive force." Journal of Differential Equations 251, no. 8 (2011): 2209–25. http://dx.doi.org/10.1016/j.jde.2011.07.008.

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31

Faria, Teresa, Rafael Obaya, and Ana M. Sanz. "Asymptotic Behaviour for a Class of Non-monotone Delay Differential Systems with Applications." Journal of Dynamics and Differential Equations 30, no. 3 (2017): 911–35. http://dx.doi.org/10.1007/s10884-017-9572-8.

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32

Reichel, Wolfgang, and Wolfgang Walter. "Sturm–Liouville Type Problems for the p-Laplacian under Asymptotic Non-resonance Conditions." Journal of Differential Equations 156, no. 1 (1999): 50–70. http://dx.doi.org/10.1006/jdeq.1998.3611.

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33

Ito, Akio, and Takashi Suzuki. "Asymptotic behavior of the solution to the non-isothermal phase separation." Nonlinear Analysis: Theory, Methods & Applications 68, no. 7 (2008): 1825–43. http://dx.doi.org/10.1016/j.na.2007.01.015.

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34

Iovane, G., A. V. Kapustyan, and J. Valero. "Asymptotic behaviour of reaction–diffusion equations with non-damped impulsive effects." Nonlinear Analysis: Theory, Methods & Applications 68, no. 9 (2008): 2516–30. http://dx.doi.org/10.1016/j.na.2007.02.002.

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35

Carvalho, Alexandre N., and Cláudia B. Gentile. "Asymptotic behaviour of non-linear parabolic equations with monotone principal part." Journal of Mathematical Analysis and Applications 280, no. 2 (2003): 252–72. http://dx.doi.org/10.1016/s0022-247x(03)00037-4.

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36

Wang, Bixiang, and Robert Jones. "Asymptotic behavior of a class of non-autonomous degenerate parabolic equations." Nonlinear Analysis: Theory, Methods & Applications 72, no. 9-10 (2010): 3887–902. http://dx.doi.org/10.1016/j.na.2010.01.026.

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37

Dix, Julio G., Christos G. Philos, and Ioannis K. Purnaras. "Asymptotic properties of solutions to linear non-autonomous neutral differential equations." Journal of Mathematical Analysis and Applications 318, no. 1 (2006): 296–304. http://dx.doi.org/10.1016/j.jmaa.2005.06.005.

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38

Jia, Xiaobiao, Dongsheng Li, and Shanshan Ma. "Asymptotic behaviors of solutions of non-divergence elliptic equations in cones." Journal of Mathematical Analysis and Applications 479, no. 2 (2019): 2256–67. http://dx.doi.org/10.1016/j.jmaa.2019.07.055.

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39

Rodríguez, M. A., A. Díaz-Guilera, and J. M. Sancho. "Asymptotic analysis of a stochastic non-linear nuclear reactor model." Annals of Nuclear Energy 13, no. 1 (1986): 49–52. http://dx.doi.org/10.1016/0306-4549(86)90116-7.

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40

Cui, Xia, Guang-wei Yuan, and Zhi-jun Shen. "Asymptotic analysis of discrete schemes for non-equilibrium radiation diffusion." Journal of Computational Physics 313 (May 2016): 415–29. http://dx.doi.org/10.1016/j.jcp.2016.02.061.

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41

Todorov, Todor D., and Hans Vernaeve. "Full algebra of generalized functions and non-standard asymptotic analysis." Logic and Analysis 1, no. 3-4 (2008): 205–34. http://dx.doi.org/10.1007/s11813-008-0008-y.

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42

Zakerzadeh, Hamed. "Asymptotic analysis of the RS-IMEX scheme for the shallow water equations in one space dimension." ESAIM: Mathematical Modelling and Numerical Analysis 53, no. 3 (2019): 893–924. http://dx.doi.org/10.1051/m2an/2019005.

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We introduce and analyse the so-called Reference Solution IMplicit-EXplicit scheme as a flux-splitting method for singularly-perturbed systems of balance laws. RS-IMEX scheme’s bottom-line is to use the Taylor expansion of the flux function and the source term around a reference solution (typically the asymptotic limit or an equilibrium solution) to decompose the flux and the source into stiff and non-stiff parts so that the resulting IMEX scheme is Asymptotic Preserving (AP) w.r.t. the singular parameter tending to zero. We prove the asymptotic consistency, asymptotic stability, solvability and well-balancing of the scheme for the case of the one-dimensional shallow water equations when the singular parameter is the Froude number. We will also study several test cases to illustrate the quality of the computed solutions and to confirm the analysis.

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43

Anguiano, María, and Tomás Caraballo. "Asymptotic behaviour of a non-autonomous Lorenz-84 system." Discrete and Continuous Dynamical Systems 34, no. 10 (2014): 3901–20. http://dx.doi.org/10.3934/dcds.2014.34.3901.

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44

Chowdhury, Indranil, and Prosenjit Roy. "On the asymptotic analysis of problems involving fractional Laplacian in cylindrical domains tending to infinity." Communications in Contemporary Mathematics 19, no. 05 (2016): 1650035. http://dx.doi.org/10.1142/s0219199716500358.

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The paper is an attempt to investigate the issues of asymptotic analysis for problems involving fractional Laplacian where the domains tend to become unbounded in one-direction. Motivated from the pioneering work on second-order elliptic problems by Chipot and Rougirel in [On the asymptotic behaviour of the solution of elliptic problems in cylindrical domains becoming unbounded, Commun. Contemp. Math. 4(1) (2002) 15–44], where the force functions are considered on the cross-section of domains, we prove the non-local counterpart of their result.Recently in [Asymptotic behavior of elliptic nonlocal equations set in cylinders, Asymptot. Anal. 89(1–2) (2014) 21–35] Yeressian established a weighted estimate for solutions of non-local Dirichlet problems which exhibit the asymptotic behavior. The case when [Formula: see text] was also treated as an example to show how the weighted estimate might be used to achieve the asymptotic behavior. In this paper, we extend this result to each order between [Formula: see text] and [Formula: see text].

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45

Erdogan, M. Burak. "Analytic and asymptotic properties of non-symmetric Linnik's probability densities." Journal of Fourier Analysis and Applications 5, no. 6 (1999): 523–44. http://dx.doi.org/10.1007/bf01257189.

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46

Wang, Lulu, and Qiaozhen Ma. "Uniform attractors of non-autonomous suspension bridge equations with memory." Electronic Journal of Differential Equations 2024, no. 01-?? (2024): 16. http://dx.doi.org/10.58997/ejde.2024.16.

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In this article, we investigate the long-time dynamical behavior of non-autonomous suspension bridge equations with memory and free boundary conditions. We first establish the well-posedness of the system by means of the maximal monotone operator theory. Secondly, the existence of uniformly bounded absorbing set is obtained. Finally, asymptotic compactness of the process is verified, and then the existence of uniform attractors is proved for non-autonomous suspension bridge equations with memory term. For more information see https://ejde.math.txstate.edu/Volumes/2024/16/abstr.html

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47

Da Silva, Severino Horacio. "Asymptotic behavior for a non-autonomous model of neural fields with variable external stimuli." Electronic Journal of Differential Equations 2020, no. 01-132 (2020): 92. http://dx.doi.org/10.58997/ejde.2020.92.

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In this work we consider the class of nonlocal non-autonomous evolution problems in a bounded smooth domain \(\Omega\) in \(\mathbb{R}^{N}\) $$\displaylines{ \partial_t u(t,x) =- a(t)u(t,x) + b(t) \int_{\mathbb{R}^N} J(x,y)f(t,u(t,y))\,dy -h +S(t,x),\quad t\geq\tau \cr u(\tau,x)=u_\tau(x), }$$ with u(t,x)= 0 for \(t\geq\tau\) and \(x \in\mathbb{R}^N\backslash\Omega\). Under appropriate assumptions we study the asymptotic behavior of the evolution process, generated by this problem in a suitable Banach space. We prove results on existence, uniqueness and smoothness of the solutions and on the existence of pullback attractor for the evolution process. We also prove a continuous dependence of the evolution process with respect to the external stimuli function present in the model. Furthermore, using the continuous dependence of the evolution process, we prove the upper semicontinuity of pullback attractors with respect to the external stimuli function. We finish this article with a small discussion about the model and about a biological interpretation of the result on the continuous dependence of neuronal activity with respect to the external stimuli function. For more information see https://ejde.math.txstate.edu/Volumes/2020/92/abstr.html

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48

Younesian, D., E. Esmailzadeh, and R. Sedaghati. "Asymptotic solutions and stability analysis for generalized non-homogeneous Mathieu equation." Communications in Nonlinear Science and Numerical Simulation 12, no. 1 (2007): 58–71. http://dx.doi.org/10.1016/j.cnsns.2006.01.005.

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49

Feng, Yue-Hong, Xin Li, Ming Mei, and Shu Wang. "Asymptotic decay of bipolar isentropic/non-isentropic compressible Navier-Stokes-Maxwell systems." Journal of Differential Equations 301 (November 2021): 471–542. http://dx.doi.org/10.1016/j.jde.2021.08.029.

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50

Ito, Akio, and Takashi Suzuki. "Asymptotic behavior of the solution to the non-isothermal phase field equation." Nonlinear Analysis: Theory, Methods & Applications 64, no. 11 (2006): 2454–79. http://dx.doi.org/10.1016/j.na.2005.08.025.

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