Relevant bibliographies by topics / Asymptotic expansions of solutions

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Asymptotic expansions of solutions'

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Published: 4 June 2021
Last updated: 3 February 2022

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Journal articles on the topic "Asymptotic expansions of solutions"

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MAJDALANI, JOSEPH. "Multiple asymptotic solutions for axially travelling waves in porous channels." Journal of Fluid Mechanics 636 (September 25, 2009): 59–89. http://dx.doi.org/10.1017/s0022112009007939.

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Travelling waves in confined enclosures, such as porous channels, develop boundary layers that evolve over varying spatial scales. The present analysis employs a technique that circumvents guessing of the inner coordinate transformations at the forefront of a multiple-scales expansion. The work extends a former study in which a two-dimensional oscillatory solution was derived for the rotational travelling wave in a porous channel. This asymptotic solution was based on a free coordinate that could be evaluated using Prandtl's principle of matching with supplementary expansions. Its derivation required matching the dominant term in the multiple-scales expansion to an available Wentzel-Kramers-Brillouin (WKB) solution. Presently, the principle of least singular behaviour is used. This approach leads to a multiple-scales approximation that can be obtained independently of supplementary expansions. Furthermore, a procedure that yields different types of WKB solutions is described and extended to arbitrary order in the viscous perturbation parameter. Among those, the WKB expansion of type I is shown to exhibit an alternating singularity at odd orders in the perturbation parameter. This singularity is identified and suppressed using matched asymptotic tools. In contrast, the WKB expansion of type II is found to be uniformly valid at any order. Additionally, matched asymptotic, WKB and multiple-scales expansions are developed for several test cases. These enable us to characterize the essential vortico-acoustic features of the axially travelling waves in a porous channel. All solutions are numerically verified, compared and discussed.
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Fahrenwaldt, Matthias A. "Short-time asymptotic expansions of semilinear evolution equations." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 146, no. 1 (January 7, 2016): 141–67. http://dx.doi.org/10.1017/s0308210515000372.

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We develop an algebraic approach to constructing short-time asymptotic expansions of solutions of a class of abstract semilinear evolution equations. The expansions are typically valid for both the solution of the equation and its gradient. We apply a perturbation approach based on the symbolic calculus of pseudo-differential operators and heat kernel methods. The construction is explicit and can be done to arbitrary order. All results are rigorously formulated in terms of Banach algebras. As an application we obtain a novel approach to finding approximate solutions of Markovian backward stochastic differential equations.
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Meftah, Safia. "A New Approach to Approximate Solutions for Nonlinear Differential Equation." International Journal of Mathematics and Mathematical Sciences 2018 (July 16, 2018): 1–8. http://dx.doi.org/10.1155/2018/5129502.

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The question discussed in this study concerns one of the most helpful approximation methods, namely, the expansion of a solution of a differential equation in a series in powers of a small parameter. We used the Lindstedt-Poincaré perturbation method to construct a solution closer to uniformly valid asymptotic expansions for periodic solutions of second-order nonlinear differential equations.
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Steinrück, Herbert. "Mixed convection over a cooled horizontal plate: non-uniqueness and numerical instabilities of the boundary-layer equations." Journal of Fluid Mechanics 278 (November 10, 1994): 251–65. http://dx.doi.org/10.1017/s0022112094003691.

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The boundary-layer flow over a cooled horizontal plate is considered. It is shown that the real part of the spectrum of the evolution operator of the linearized equations is not bounded uniformly from above which explains the difficulties encounterd by a numerical solution. Furthermore it is shown that near the leading edge an asymptotic expansion of the solution is not unique. A one-parametric family of asymptotic expansions of solutions can be constructed.
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Archibasov, A. A. "ASYMPTOTIC EXPANSIONS OF SOLUTIONS FOR HIV EVOLUTION MODEL." Vestnik of Samara University. Natural Science Series 19, no. 3 (June 1, 2017): 5–11. http://dx.doi.org/10.18287/2541-7525-2013-19-3-5-11.

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In the paper the mathematical model of HIV evolution is considered. This model is a singularly perturbed partial integro-differential equations system. Based on the Tikhonov—Vasilieva method of boundary function the first approximation of the system solutions is realized.
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Geng, Jun, and Zhongwei Shen. "Asymptotic expansions of fundamental solutions in parabolic homogenization." Analysis & PDE 13, no. 1 (January 6, 2020): 147–70. http://dx.doi.org/10.2140/apde.2020.13.147.

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Samovol, V. S. "Asymptotic Expansions of Solutions to the Riccati Equation." Doklady Mathematics 101, no. 1 (January 2020): 49–52. http://dx.doi.org/10.1134/s1064562420010196.

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Ishige, Kazuhiro, Tatsuki Kawakami, and Hironori Michihisa. "Asymptotic Expansions of Solutions of Fractional Diffusion Equations." SIAM Journal on Mathematical Analysis 49, no. 3 (January 2017): 2167–90. http://dx.doi.org/10.1137/16m1101428.

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Schulz, Friedmar. "Asymptotic expansions for solutions of elliptic differential inequalities." Analysis 14, no. 2-3 (September 1994): 139–46. http://dx.doi.org/10.1524/anly.1994.14.23.139.

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Caflisch, R. E. "Asymptotic expansions of solutions for the Boltzmann equation." Transport Theory and Statistical Physics 16, no. 4-6 (June 1987): 701–25. http://dx.doi.org/10.1080/00411458708204310.

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Dissertations / Theses on the topic "Asymptotic expansions of solutions"

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Xiaochun, Liu, and Ingo Witt. "Asymptotic expansions for bounded solutions to semilinear Fuchsian equations." Universität Potsdam, 2001. http://opus.kobv.de/ubp/volltexte/2008/2591/.

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It is shown that bounded solutions to semilinear elliptic Fuchsian equations obey complete asymptoic expansions in terms of powers and logarithms in the distance to the boundary. For that purpose, Schuze's notion of asymptotic type for conormal asymptotics close to a conical point is refined. This in turn allows to perform explicit calculations on asymptotic types - modulo the resolution of the spectral problem for determining the singular exponents in the asmptotic expansions.
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Höppner, Reinhard Höppner Reinhard Höppner Reinhard. "Asymptotic and hyperasymptotic expansions of solutions of linear differential equations near irregular singular points of higher rank." [S.l.] : [s.n.], 2001. http://deposit.ddb.de/cgi-bin/dokserv?idn=962883921.

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Hoeppner, Reinhard. "Asymptotic and hyperasymptotic expansions of solutions of linear differential equations near irregular singular points of higher rank." [S.l. : s.n.], 2001. http://deposit.ddb.de/cgi-bin/dokserv?idn=962883921.

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Hoang, Luan Thach. "Asymptotic expansions of the regular solutions to the 3D Navier-Stokes equations and applications to the analysis of the helicity." Diss., Texas A&M University, 2005. http://hdl.handle.net/1969.1/2355.

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A new construction of regular solutions to the three dimensional Navier{Stokes equa- tions is introduced and applied to the study of their asymptotic expansions. This construction and other Phragmen-Linderl??of type estimates are used to establish su??- cient conditions for the convergence of those expansions. The construction also de??nes a system of inhomogeneous di??erential equations, called the extended Navier{Stokes equations, which turns out to have global solutions in suitably constructed normed spaces. Moreover, in these spaces, the normal form of the Navier{Stokes equations associated with the terms of the asymptotic expansions is a well-behaved in??nite system of di??erential equations. An application of those asymptotic expansions of regular solutions is the analysis of the helicity for large times. The dichotomy of the helicity's asymptotic behavior is then established. Furthermore, the relations between the helicity and the energy in several cases are described.
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Masaki, Satoshi. "Asymptotic expansion of solutions to the nonlinear Schrödinger equation with power nonlinearity." 京都大学 (Kyoto University), 2009. http://hdl.handle.net/2433/124383.

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Starkloff, Hans-Jörg, and Ralf Wunderlich. "Stationary solutions of linear ODEs with a randomly perturbed system matrix and additive noise." Universitätsbibliothek Chemnitz, 2005. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200501335.

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The paper considers systems of linear first-order ODEs with a randomly perturbed system matrix and stationary additive noise. For the description of the long-term behavior of such systems it is necessary to study their stationary solutions. We deal with conditions for the existence of stationary solutions as well as with their representations and the computation of their moment functions. Assuming small perturbations of the system matrix we apply perturbation techniques to find series representations of the stationary solutions and give asymptotic expansions for their first- and second-order moment functions. We illustrate the findings with a numerical example of a scalar ODE, for which the moment functions of the stationary solution still can be computed explicitly. This allows the assessment of the goodness of the approximations found from the derived asymptotic expansions.
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Arazy, Jonathan, Bent Orsted, and jarazy@math haifa ac il. "Asymptotic Expansions of Berezin Transforms." ESI preprints, 2000. ftp://ftp.esi.ac.at/pub/Preprints/esi922.ps.

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Chapman, Frederick William. "Theory and applications of dual asymptotic expansions." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape15/PQDD_0003/MQ32870.pdf.

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Kosad, Youssouf. "Analyse spectrale et comportement asymptotique des solutions de quelques modèles d’équations de transport." Thesis, Université Clermont Auvergne‎ (2017-2020), 2017. http://www.theses.fr/2017CLFAC056/document.

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Cette thèse est consacrée à la théorie spectrale de quelques opérateurs de transport et le comportement asymptotique (pour les temps grands) des solutions des problèmes de Cauchy gouvernés par ces derniers. Dans la première partie, on s'est intéressé aux propriétés spectrales des opérateurs d'advection et de transport des neutrons dans le cadre multidimensionnel pour des conditions aux limites générales. Après avoir établi un résultat de compacité de type lemmes de moyenne indispensable dans notre analyse, on a donné entre autre une description fine du spectre asymptotique de l'opérateur de transport. Ce travail a été complété par l'étude des propriétés de régularité et le comportement asymptotique de la solution du problème de Cauchy gouverné par l'opérateur de transport étudié précédemment pour des conditions aux limites de type bounce-back plus un opérateur compact dans l'espace L^1. Ensuite, on a étudié le caractère bien posé et le comportement asymptotique de la solution d'une équation de transport des neutrons avec des sections efficaces non bornées. Contrairement à la première partie, l'analyse de ce problème nécessite l'usage d'une théorie de perturbation de Miyadera-Voigt pour les opérateurs non bornés. La dernière partie de ce travail porte sur un problème linéaire issu d'un modèle introduit en 1974 par Lebowitz et Rubinow décrivant la prolifération d'une population de cellules structuré par l'âge et la longueur du cycle. Notre analyse a porté sur le cas où la longueur du cycle maximale est infinie
This thesis is devoted to the spectral theory and the time asymptotic behavior of the solution to Cauchy problems governed by various transport operators. In the first part, we discussed the spectral properties of streaming and transport operators in finite bodies with general boundary conditions. After establishing a compactness result essential to our analysis, we gave a fine description of the asymptotic spectrum of the transport operator. We also derive the regularity and the asymptotic behavior of the solution to Cauchy problem governed by the transport operator supplemented by bounce-back boundary conditions plus a compact operator in the space L^1. In the second part, we discussed the well-posedness and the asymptotic behavior of the solution to Cauchy problem governed by a singular transport operator. Unlike the first part, the analysis of this problem requires the use of Miyadera-Voigt perturbation theory for unbounded operators. In the last part of this work, a Cauchy problem governed by a linear operator introduced by Lebowitz and Rubinow describing a proliferating cell population structured by age and the cycle length was considered. Here our analysis was devoted to the case where the maximum cycle length is infinite
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Petersson, Mikael. "Asymptotic Expansions for Perturbed Discrete Time Renewal Equations." Licentiate thesis, Stockholms universitet, Matematiska institutionen, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-95490.

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In this thesis we study the asymptotic behaviour of the solution of a discrete time renewal equation depending on a small perturbation parameter. In particular, we construct asymptotic expansions for the solution of the renewal equation and related quantities. The results are applied to studies of quasi-stationary phenomena for regenerative processes and asymptotics of ruin probabilities for a discrete time analogue of the Cramér-Lundberg risk model.
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Books on the topic "Asymptotic expansions of solutions"

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Matched asymptotic expansions: Ideas and techniques. New York: Springer-Verlag, 1988.

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Harabetian, Eduard. Matched asymptotic expansions to similarity solutions of shock diffraction. Hampton, Va: ICASE, 1985.

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Asymptotic behaviour of solutions of evolutionary equations. Cambridge: Cambridge University Press, 1992.

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Lagerstrom, P. A. Matched asymptotic expansion: Ideas and techniques. New York: Springer-Verlag, 1988.

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Matching of asymptotic expansions of solutions of boundary value problems. Providence, R.I: American Mathematical Society, 1992.

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Ilʹin, A. M. Matching of asymptotic expansions of solutions of boundary value problems. Providence, R.I: American Mathematical Society, 1992.

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Soglasovanie asimptoticheskikh razlozheniĭ resheniĭ kraevykh zadach. Moskva: "Nauka," Glav. red. fiziko-matematicheskoĭ lit-ry, 1989.

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Asymptotics and special functions. Wellesley, Mass: A.K. Peters, 1997.

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Perturbation methods. New York: John Wiley & Sons, 2000.

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Dix, Daniel Beach. Large-time behavior of solutions of linear dispersive equations. Berlin: Springer, 1997.

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Book chapters on the topic "Asymptotic expansions of solutions"

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Bouche, Daniel, Frédéric Molinet, and Raj Mittra. "Search for Solutions in the Form of Asymptotic Expansions." In Asymptotic Methods in Electromagnetics, 91–120. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/978-3-642-60517-8_2.

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Yin, G. George, and Qing Zhang. "Asymptotic Expansions of Solutions for Forward Equations." In Continuous-Time Markov Chains and Applications, 59–140. New York, NY: Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-4346-9_4.

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Yin, G. George, and Qing Zhang. "Asymptotic Expansions of Solutions for Backward Equations." In Continuous-Time Markov Chains and Applications, 235–57. New York, NY: Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-4346-9_6.

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Kuzmina, R. P. "Solution Expansions of the Quasiregular Cauchy Problem." In Asymptotic Methods for Ordinary Differential Equations, 3–82. Dordrecht: Springer Netherlands, 2000. http://dx.doi.org/10.1007/978-94-015-9347-2_1.

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Schulze, B. W. "Mellin expansions of pseudo-differential operators and conormal asymptotics of solutions." In Pseudo-Differential Operators, 378–401. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/bfb0077752.

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Bourbaki, Nicolas. "Asymptotic Expansions." In Elements of the History of Mathematics, 199–202. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/978-3-642-61693-8_18.

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Gzyl, Henryk. "Asymptotic Expansions." In Diffusions and Waves, 135–54. Dordrecht: Springer Netherlands, 2002. http://dx.doi.org/10.1007/978-94-010-0293-6_7.

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Hsieh, Po-Fang, and Yasutaka Sibuya. "Asymptotic Expansions." In Universitext, 342–71. New York, NY: Springer New York, 1999. http://dx.doi.org/10.1007/978-1-4612-1506-6_11.

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Dhrymes, Phoebus J. "Asymptotic Expansions." In Mathematics for Econometrics, 393–409. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-8145-4_13.

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Jiang, Jiming. "Asymptotic Expansions." In Springer Texts in Statistics, 81–126. New York, NY: Springer New York, 2010. http://dx.doi.org/10.1007/978-1-4419-6827-2_4.

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Conference papers on the topic "Asymptotic expansions of solutions"

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Popivanov, Nedyu, Todor Popov, and Allen Tesdall. "Semi-Fredholm solvability and asymptotic expansions of singular solutions for Protter problems." In 39TH INTERNATIONAL CONFERENCE APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS AMEE13. AIP, 2013. http://dx.doi.org/10.1063/1.4854774.

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Kudish, Ilya I. "Plane EHL Problems for Pre-Critical Heavy-Loaded Contact: Stable Numerical Solutions." In STLE/ASME 2008 International Joint Tribology Conference. ASMEDC, 2008. http://dx.doi.org/10.1115/ijtc2008-71106.

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The paper is aimed at considering the classic isothermal plane EHL problem for heavy-loaded contacts lubricated by Newtonian and non-Newtonian fluids. The analytical analysis of the problem is based on matched asymptotic expansions. For pre-critical lubrication regimes asymptotic equations for pressure and gap are derived and solved numerically in the inlet and exit zones. The number of input parameters in asymptotic equations is reduced. The numerical solutions are stable. Formulas for lubrication film thickness for Newtonian and non-Newtonian fluids for pre- and over-critical regimes are derived based on the asymptotic analysis.
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POPOVIĆ, NIKOLA. "A GEOMETRIC ANALYSIS OF THE LAGERSTROM MODEL: EXISTENCE OF SOLUTIONS AND RIGOROUS ASYMPTOTIC EXPANSIONS." In Proceedings of the International Conference on Differential Equations. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812702067_0151.

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YOSHINO, KUNIO, and YASUYUKI OKA. "ASYMPTOTIC EXPANSIONS OF THE SOLUTIONS TO THE HEAT EQUATIONS WITH GENERALIZED FUNCTIONS INITIAL VALUE." In Proceedings of the Conference Satellite to ICM 2006. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812778833_0020.

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ISHIMURA, N., and K. NISHIDA. "ASYMPTOTIC EXPANSION METHOD FOR LOCAL VOLATILITY MODELS." In The International Conference on Reaction-Diffusion System and Viscosity Solutions. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789812834744_0006.

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Happawana, G. S., A. K. Bajaj, and O. D. I. Nwokah. "A Singular Perturbation Analysis of Eigenvalue Veering and Mode Localization in Perturbed Linear Chain and Cyclic Systems." In ASME 1991 Design Technical Conferences. American Society of Mechanical Engineers, 1991. http://dx.doi.org/10.1115/detc1991-0206.

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Abstract An investigation into the eigenvalue loci veering and mode localization phenomenon is presented for mistuned structural systems. Examples from both, the weakly coupled uniaxial component systems and the cyclic symmetric systems, are considered. The analysis is based on singular perturbation techniques. It is shown that uniform asymptotic expansions for the eigenvalues and eigenvectors can be constructed in terms of the mistuning parameters, and these solutions are in excellent agreement with the exact solutions. The asymptotic expansions are then used to clearly show how the singular behavior in the eigenfunctions or modeshapes leads to mode localization.
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JÄRV, L., P. KUUSK, and M. SAAL. "SUPER-ACCELERATED EXPANSION AND ASYMPTOTIC SOLUTIONS IN SCALAR-TENSOR COSMOLOGY." In Proceedings of the MG12 Meeting on General Relativity. WORLD SCIENTIFIC, 2012. http://dx.doi.org/10.1142/9789814374552_0408.

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Kudish, Ilya I. "Classic Plane EHL Problem for Pre-Critical Heavy-Loaded Contacts." In ASME 2008 9th Biennial Conference on Engineering Systems Design and Analysis. ASMEDC, 2008. http://dx.doi.org/10.1115/esda2008-59240.

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The paper is aimed at considering the classic plane EHL problem for heavy-loaded contacts lubricated by Newtonian and non-Newtonian fluids. The analytical analysis of the problem is based on matched asymptotic expansions. It is shown that depending on the behavior of the lubricant viscosity there are two distinct lubrication regimes: pre- and over-critical regimes. A specific way for determining which regime occurs for given conditions is proposed. For these two lubrication regimes the relationships of the mechanical mechanisms determining the solution are different and, therefore, the solution structures for the two regimes are different. Asymptotic equations for pressure and gap are derived and solved numerically for pre-critical regimes in the inlet and exit zones. The numerical solutions are stable. Formulas for lubrication film thickness for Newtonian and non-Newtonian fluids for pre- and over-critical regimes are derived based on the asymptotic analysis.
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Raman, Arvind, Patricia Davies, and Anil K. Bajaj. "Analytical Prediction of Nonlinear System Response to Non-Stationary Excitations." In ASME 1993 Design Technical Conferences. American Society of Mechanical Engineers, 1993. http://dx.doi.org/10.1115/detc1993-0127.

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Abstract The study of the non-stationary response of systems has many applications in problems related to transition through resonance in rotating machinery, aerospace structures and other physical systems. In this paper, we present methods to analytically predict the response of some weakly nonlinear systems to slowly varying parameter changes. We consider systems which can be averaged and represented as two first order equations. The evolution of the solutions of such systems through critical (jump or bifurcation) points is studied using the method of matched asymptotic expansions. As an example, the method is used to predict the response of the forced Duffing’s oscillator during passage through resonance. Starting with a general system of two, first-order equations, we set up a slowly varying equilibrium or ‘outer’ solution as an asymptotic expansion about the stationary solution. This solution is seen to be invalid in a small neighborhood of the critical points — the ‘inner’ region. In this inner layer, the system of equations is transformed into the Jordan canonical form, which is easier to study. Using approximations from the center manifold theory, the problem is reduced to one first-order equation. By making appropriate scale changes, an ‘inner’ solution is developed. This solution is asymptotically matched with the outer expansion to yield a unified solution valid for all time.
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Nikolov, Aleksey, and Nedyu Popivanov. "Asymptotic expansion of singular solutions to Protter problem for (2+1)-D degenerate wave equation." In 39TH INTERNATIONAL CONFERENCE APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS AMEE13. AIP, 2013. http://dx.doi.org/10.1063/1.4854763.

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Reports on the topic "Asymptotic expansions of solutions"

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Bather, John, and Herman Chernoff. Bounds and Asymptotic Expansions for Solutions of the Free Boundary Problems Related to Sequential Decision Versions of a Bioequivalence Problem. Fort Belvoir, VA: Defense Technical Information Center, November 1993. http://dx.doi.org/10.21236/ada273551.

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Mudaliar, Saba. Asymptotic Expansions for a Class of Hypergeometric Functions. Fort Belvoir, VA: Defense Technical Information Center, August 1992. http://dx.doi.org/10.21236/ada280374.

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Mane S. R. SOLUTIONS OF LAPLACES EQUATION AND MULTIPOLE EXPANSIONS WITH A CURVED LONGITUDINAL AXIS. Office of Scientific and Technical Information (OSTI), November 1991. http://dx.doi.org/10.2172/1151263.

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Yanovski, Alexander B. • Expansions Over Adjoint Solutions for the Caudrey-Beals-Coifman System with Reductions of Mikhailov Type. GIQ, 2013. http://dx.doi.org/10.7546/giq-14-2013-253-268.

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Wilkes, James M. Mechanics of a Near Net-Shape Stress-Coated Membrane. Volume I of II: Theory Development Using the Method of Asymptotic Expansions. Fort Belvoir, VA: Defense Technical Information Center, December 2002. http://dx.doi.org/10.21236/ada414465.

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Yanovski, Alexandar. Recursion Operators and Expansions Over Adjoint Solutions for the Caudrey-Beals-Coifman System with Reductions of Mikhailov Type. Journal of Geometry and Symmetry in Physics, 2013. http://dx.doi.org/10.7546/jgsp-30-2013-105-120.

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Dresner, L. Asymptotic behavior of solutions of diffusion-like partial differential equations invariant to a family of affine groups. Office of Scientific and Technical Information (OSTI), July 1990. http://dx.doi.org/10.2172/6697591.

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Pocher, Liam, Nathaniel Morgan, Travis Peery, and Jonathan Mace. Analysis into Asymptotic Convergence to Full Nonlinear Solutions and Exploration of the Implication of Numerical Operator Mutation of Differential Systems. Office of Scientific and Technical Information (OSTI), August 2020. http://dx.doi.org/10.2172/1648057.

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