Relevant bibliographies by topics / Second order elliptic equation

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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 'Second order elliptic equation'

Author: Grafiati
Published: 5 June 2025
Last updated: 2 August 2025

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Journal articles on the topic "Second order elliptic equation"

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Boughazi, Hichem. "Second-Order Elliptic Equation with Singularities." International Journal of Differential Equations 2020 (May 20, 2020): 1–16. http://dx.doi.org/10.1155/2020/4589864.

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On the compact Riemannian manifold of dimension n≥5, we study the existence and regularity of nontrivial solutions for nonlinear second-order elliptic equation with singularities. At the end, we give a geometric application of the above singular equation.
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Farg, Ahmed Saeed, A. M. Abd Elbary, and Tarek A. Khalil. "Applied method of characteristics on 2nd order linear P.D.E." Journal of Physics: Conference Series 2304, no. 1 (2022): 012003. http://dx.doi.org/10.1088/1742-6596/2304/1/012003.

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Abstract PDEs are very important in dynamics, aerodynamics, elasticity, heat transfer, waves, electromagnetic theory, transmission lines, quantum mechanics, weather forecasting, prediction of crime places, disasters, how universe behave ……. Etc., second order linear PDEs can be classified according to the characteristic equation into 3 types hyperbolic, parabolic and elliptic; Hyperbolic equations have two distinct families of (real) characteristic curves, parabolic equations have a single family of characteristic curves, and the elliptic equations have none. All the three types of equations c
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Shan, Jin. "Singularly perturbed nonlinear second order elliptic equation." Applied Mathematics and Mechanics 8, no. 6 (1987): 547–59. http://dx.doi.org/10.1007/bf02017404.

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Azaiz, Seid, Hichem Boughazi, and Kamel Tahri. "On the singular second-order elliptic equation." Journal of Mathematical Analysis and Applications 489, no. 1 (2020): 124077. http://dx.doi.org/10.1016/j.jmaa.2020.124077.

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Caffarelli, Luis. "Elliptic second order equations." Rendiconti del Seminario Matematico e Fisico di Milano 58, no. 1 (1988): 253–84. http://dx.doi.org/10.1007/bf02925245.

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Tokibetov, Zh A., N. E. Bashar, and А. К. Pirmanova. "THE CAUCHY-DIRICHLET PROBLEM FOR A SYSTEM OF FIRST-ORDER EQUATIONS." BULLETIN Series of Physics & Mathematical Sciences 72, no. 4 (2020): 68–72. http://dx.doi.org/10.51889/2020-4.1728-7901.10.

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For a single second-order elliptic partial differential equation with sufficiently smooth coefficients, all classical boundary value problems that are correct for the Laplace equations are Fredholm. The formulation of classical boundary value problems for the laplace equation is dictated by physical applications. The simplest of the boundary value problems for the Laplace equation is the Dirichlet problem, which is reduced to the problem of the field of charges distributed on a certain surface. The Dirichlet problem for partial differential equations in space is usually called the Cauchy-Diric
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Potts, Renfrey B. "Weierstrass elliptic difference equations." Bulletin of the Australian Mathematical Society 35, no. 1 (1987): 43–48. http://dx.doi.org/10.1017/s0004972700013022.

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The Weierstrass elliptic function satisfies a nonlinear first order and a nonlinear second order differential equation. It is shown that these differential equations can be discretized in such a way that the solutions of the resulting difference equations exactly coincide with the corresponding values of the elliptic function.
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Burazin, Krešimir, Jelena Jankov, and Marko Vrdoljak. "HOMOGENIZATION OF ELASTIC PLATE EQUATION∗." Mathematical Modelling and Analysis 23, no. 2 (2018): 190–204. http://dx.doi.org/10.3846/mma.2018.012.

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We are interested in general homogenization theory for fourth-order elliptic equation describing the Kirchhoff model for pure bending of a thin solid symmetric plate under a transverse load. Such theory is well-developed for second-order elliptic problems, while some results for general elliptic equations were established by Zhikov, Kozlov, Oleinik and Ngoan (1979). We push forward an approach of Antoni´c and Balenovi´c (1999, 2000) by proving a number of properties of H-convergence for stationary plate equation.
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Ashyralyev, Allaberen, and Okan Gercek. "On the Second Order of Accuracy Stable Implicit Difference Scheme for Elliptic-Parabolic Equations." Abstract and Applied Analysis 2012 (2012): 1–13. http://dx.doi.org/10.1155/2012/230190.

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We are interested in studying a second order of accuracy implicit difference scheme for the solution of the elliptic-parabolic equation with the nonlocal boundary condition. Well-posedness of this difference scheme is established. In an application, coercivity estimates in Hölder norms for approximate solutions of multipoint nonlocal boundary value problems for elliptic-parabolic differential equations are obtained.
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SAMARSKII, ALEKSANDR A., and PETER N. VABISHCHEVICH. "REGULARIZED DIFFERENCE SCHEMES FOR EVOLUTIONARY SECOND ORDER EQUATIONS." Mathematical Models and Methods in Applied Sciences 02, no. 03 (1992): 295–315. http://dx.doi.org/10.1142/s0218202592000193.

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The questions of approximate solution of unstable problems for evolutionary second order equations are discussed in this paper. The classical Cauchy problem for elliptic type equation is a significant example of such problem. Incorrectness of this problem (the Hadamard example) is due to instability of the solution towards small perturbations of the initial conditions. The extension problem of the solutions of well-posed elliptic problems beyond the calculation region boundary is also discussed. The stability of corresponding difference schemes is investigated by basing on general theory of ρ-
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Dissertations / Theses on the topic "Second order elliptic equation"

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MONTEIRO, GABRIEL DE LIMA. "WEAK SOLUTIONS FOR ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS OF SECOND ORDER." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2018. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=36023@1.

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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO<br>COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR<br>PROGRAMA DE SUPORTE À PÓS-GRADUAÇÃO DE INSTS. DE ENSINO<br>PROGRAMA DE EXCELENCIA ACADEMICA<br>Esse trabalho tem como objetivo ser uma introdução ao estudo da existência e unicidade de soluções fracas para equações diferenciais parciais elípticas. Começamos definindo o espaço de Sobolev para, a partir da definição, provarmos algumas propriedades básicas que nos ajudarão no estudo das equações diferenciais parciais elípticas. Finalizamos com o desenvolvimento do Teorema de Lax-M
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Mavinga, Nsoki. "Nonlinear second order parabolic and elliptic equations with nonlinear boundary conditions." Birmingham, Ala. : University of Alabama at Birmingham, 2008. https://www.mhsl.uab.edu/dt/2009r/mavinga.pdf.

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Thesis (Ph. D.)--University of Alabama at Birmingham, 2008.<br>Title from PDF title page (viewed Sept. 23, 2009). Additional advisors: Inmaculada Aban, Alexander Frenkel, Wenzhang Huang, Yanni Zeng. Includes bibliographical references.
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Zhuang, Qiao. "Immersed Finite Elements for a Second Order Elliptic Operator and Their Applications." Diss., Virginia Tech, 2020. http://hdl.handle.net/10919/99040.

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This dissertation studies immersed finite elements (IFE) for a second order elliptic operator and their applications to interface problems of related partial differential equations. We start with the immersed finite element methods for the second order elliptic operator with a discontinuous coefficient associated with the elliptic interface problems. We introduce an energy norm stronger than the one used in [111]. Then we derive an estimate for the IFE interpolation error with this energy norm using patches of interface elements. We prove both the continuity and coercivity of the bilinear for
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Teka, Kubrom Hisho. "The obstacle problem for second order elliptic operators in nondivergence form." Diss., Kansas State University, 2012. http://hdl.handle.net/2097/14035.

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Doctor of Philosophy<br>Department of Mathematics<br>Ivan Blank<br>We study the obstacle problem with an elliptic operator in nondivergence form with principal coefficients in VMO. We develop all of the basic theory of existence, uniqueness, optimal regularity, and nondegeneracy of the solutions. These results, in turn, allow us to begin the study of the regularity of the free boundary, and we show existence of blowup limits, a basic measure stability result, and a measure-theoretic version of the Caffarelli alternative proven in Caffarelli's 1977 paper ``The regularity of free boundaries in
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Fontana, Eleonora. "Maximum Principle for Elliptic and Parabolic Equations." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2016. http://amslaurea.unibo.it/12061/.

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Nel primo capitolo si riporta il principio del massimo per operatori ellittici. Sarà considerato, in un primo momento, l'operatore di Laplace e, successivamente, gli operatori ellittici del secondo ordine, per i quali si dimostrerà anche il principio del massimo di Hopf. Nel secondo capitolo si affronta il principio del massimo per operatori parabolici e lo si utilizza per dimostrare l'unicità delle soluzioni di problemi ai valori al contorno.
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Pefferly, Robert J. "Finite difference approximations of second order quasi-linear elliptic and hyperbolic stochastic partial differential equations." Thesis, University of Edinburgh, 2001. http://hdl.handle.net/1842/11244.

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This thesis covers topics such as finite difference schemes, mean-square convergence, modelling, and numerical approximations of second order quasi-linear stochastic partial differential equations (SPDE) driven by white noise in less than three space dimensions. The motivation for discussing and expanding these topics lies in their implications in such physical phenomena as signal and information flow, gravitational and electromagnetic fields, large scale weather systems, and macro-computer networks. Chapter 2 delves into the hyperbolic SPDE in one space and one time dimension. This is an impo
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ABATANGELO, LAURA. "Multiplicity of solutions to elliptic equations the case of singular potentials in second order problems and morse theory in a fourth order problem." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2011. http://hdl.handle.net/10281/20336.

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Symmetry properties of solutions to some nonlinear Schroedinger equations are investigated. In particular, here the Laplace operator is perturbed by singular potentials which do not belong to the Kato class. A result of symmetry breaking of solutions is obtained provided a preliminary theorem about biradial solutions is stated. Further, a problem involving the biharmonic operator and exponential nonlinearity in dimension 4 is studied, connecting degree counting formulas with direct methods of calculus of variations via Morse theory and deformation lemmas.
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Shlapunov, Alexander, and Nikolai Tarkhanov. "Sturm-Liouville problems in domains with non-smooth edges." Universität Potsdam, 2013. http://opus.kobv.de/ubp/volltexte/2013/6733/.

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We consider a (generally, non-coercive) mixed boundary value problem in a bounded domain for a second order elliptic differential operator A. The differential operator is assumed to be of divergent form and the boundary operator B is of Robin type. The boundary is assumed to be a Lipschitz surface. Besides, we distinguish a closed subset of the boundary and control the growth of solutions near this set. We prove that the pair (A,B) induces a Fredholm operator L in suitable weighted spaces of Sobolev type, the weight function being a power of the distance to the singular set. Moreover, we prove
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Maad, Sara. "Critical point theory with applications to semilinear problems without compactness." Doctoral thesis, Uppsala : Matematiska institutionen, Univ. [distributör], 2002. http://publications.uu.se/theses/91-506-1557-2/.

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Li, Boning. "Extending the scaled boundary finite-element method to wave diffraction problems." University of Western Australia. School of Civil and Resource Engineering, 2007. http://theses.library.uwa.edu.au/adt-WU2007.0173.

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[Truncated abstract] The study reported in this thesis extends the scaled boundary finite-element method to firstorder and second-order wave diffraction problems. The scaled boundary finite-element method is a newly developed semi-analytical technique to solve systems of partial differential equations. It works by employing a special local coordinate system, called scaled boundary coordinate system, to define the computational field, and then weakening the partial differential equation in the circumferential direction with the standard finite elements whilst keeping the equation strong in the
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Books on the topic "Second order elliptic equation"

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Wang, Mingxin, and Peter Y. H. Pang. Nonlinear Second Order Elliptic Equations. Springer Nature Singapore, 2024. http://dx.doi.org/10.1007/978-981-99-8692-7.

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Gilbarg, David, and Neil S. Trudinger. Elliptic Partial Differential Equations of Second Order. Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-642-61798-0.

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Gilbarg, David. Elliptic partial differential equations of second order. 2nd ed. Springer, 1998.

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author, Véron Laurent, ed. Nonlinear second order elliptic equations involving measures. Walter de Gruyter GmbH & Co. KG, 2014.

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1942-, Trudinger Neil S., ed. Elliptic partial differential equations of second order. 2nd ed. Springer, 1998.

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Landis, E. M. Second order equations of elliptic and parabolic type. American Mathematical Society, 1998.

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Krylov, N. V. Nonlinear elliptic and parabolic equations of the second order. D. Reidel Pub. Co., 1987.

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Krylov, N. V. Nonlinear Elliptic and Parabolic Equations of the Second Order. Springer Netherlands, 1987. http://dx.doi.org/10.1007/978-94-010-9557-0.

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Barrenechea, Gabriel R., Volker John, and Petr Knobloch. Monotone Discretizations for Elliptic Second Order Partial Differential Equations. Springer Nature Switzerland, 2025. https://doi.org/10.1007/978-3-031-80684-1.

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Veron, Laurent. Singularities of solutions of second order quasilinear equations. Longman, 1996.

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Book chapters on the topic "Second order elliptic equation"

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Gilbarg, David, and Neil S. Trudinger. "Laplace’s Equation." In Elliptic Partial Differential Equations of Second Order. Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-642-61798-0_2.

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Edmunds, David E., and W. Desmond Evans. "Second-Order Elliptic Equations." In Springer Monographs in Mathematics. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-02125-2_3.

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Evans, Lawrence. "Second-order elliptic equations." In Graduate Studies in Mathematics. American Mathematical Society, 2010. http://dx.doi.org/10.1090/gsm/019/06.

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Cuvelier, C., A. Segal, and A. A. van Steenhoven. "Second Order Elliptic PDEs." In Finite Element Methods and Navier-Stokes Equations. Springer Netherlands, 1986. http://dx.doi.org/10.1007/978-94-010-9333-0_11.

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Valli, Alberto. "Second Order Linear Elliptic Equations." In UNITEXT. Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-35976-7_2.

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Smoller, Joel. "Second-Order Linear Elliptic Equations." In Grundlehren der mathematischen Wissenschaften. Springer New York, 1994. http://dx.doi.org/10.1007/978-1-4612-0873-0_8.

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Valli, Alberto. "Second Order Linear Elliptic Equations." In UNITEXT. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-58205-0_2.

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Gilbarg, David, and Neil S. Trudinger. "Poisson’s Equation and the Newtonian Potential." In Elliptic Partial Differential Equations of Second Order. Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-642-61798-0_4.

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Wang, Mingxin, and Peter Y. H. Pang. "Preliminaries." In Nonlinear Second Order Elliptic Equations. Springer Nature Singapore, 2024. http://dx.doi.org/10.1007/978-981-99-8692-7_1.

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Wang, Mingxin, and Peter Y. H. Pang. "Eigenvalue Problems of Second Order Linear Elliptic Operators." In Nonlinear Second Order Elliptic Equations. Springer Nature Singapore, 2024. http://dx.doi.org/10.1007/978-981-99-8692-7_2.

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Conference papers on the topic "Second order elliptic equation"

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Guenneau, S., E. Cherkaev, and N. Wellander. "A Second Order Homogenized Dispersive Wave Equation in a Quasiperiodic Medium." In 2024 Eighteenth International Congress on Artificial Materials for Novel Wave Phenomena (Metamaterials). IEEE, 2024. http://dx.doi.org/10.1109/metamaterials62190.2024.10703230.

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Otelbaev, Mukhtarbay, and Kordan Nauryzhanovich Ospanov. "Differentiable solutions of the second order elliptic equation." In INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2014). AIP Publishing LLC, 2014. http://dx.doi.org/10.1063/1.4893796.

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Reis, Rifat, and Adiguzel A. Dosiyev. "A fourth order accurate difference method for solving the second order elliptic equation with integral boundary condition." In INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2020). AIP Publishing, 2021. http://dx.doi.org/10.1063/5.0040375.

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Tunitsky, Dmitry V. "On Solvability of Second-Order Semilinear Elliptic Equations on Spheres." In 2021 14th International Conference Management of large-scale system development (MLSD). IEEE, 2021. http://dx.doi.org/10.1109/mlsd52249.2021.9600203.

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Turmetov, Batirkhan Kh, Maira D. Koshanova, and Moldir A. Muratbekova. "On periodic boundary value problems with an inclined derivative for a second-order elliptic equation." In INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2020). AIP Publishing, 2021. http://dx.doi.org/10.1063/5.0040263.

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Haichun Li and Yulong Zhang. "Variational approach to second-order impulsive elliptic equations with periodic boundary value problems." In 2011 International Conference on Electric Information and Control Engineering (ICEICE). IEEE, 2011. http://dx.doi.org/10.1109/iceice.2011.5777683.

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Chen, Yiming, Rao Li, Fengxia Zeng, and Wanshuai Zhao. "The Existence and Uniqueness of the Solution for a Kind of Second Order Elliptic Differential Equation of Variable Coefficient." In 2008 3rd International Conference on Innovative Computing Information and Control. IEEE, 2008. http://dx.doi.org/10.1109/icicic.2008.665.

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Liu, Xiao-qi, and Qi-ding Zhu. "MultiScale Asymptotic Analysis Method with High Accuracy for the Second Order Elliptic Equation with Oscillating Periodic Coefficients in Perforated Domain." In 2009 International Conference on Artificial Intelligence and Computational Intelligence. IEEE, 2009. http://dx.doi.org/10.1109/aici.2009.452.

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Gercek, Okan, and Emel Zusi. "On the well-posedness of a second order difference scheme for elliptic-parabolic equations in Hölder spaces." In ADVANCEMENTS IN MATHEMATICAL SCIENCES: Proceedings of the International Conference on Advancements in Mathematical Sciences. AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4930475.

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Duan, Zhipeng. "Second-Order Gaseous Flow Models in Long Circular and Noncircular Microchannels and Nanochannels." In ASME 2011 9th International Conference on Nanochannels, Microchannels, and Minichannels. ASMEDC, 2011. http://dx.doi.org/10.1115/icnmm2011-58040.

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Gaseous flow in circular and noncircular microchannels has been examined and a simple analytical model with second-order slip boundary conditions for normalized Poiseuille number is proposed. The model is applicable to arbitrary length scale. It extends previous studies to the transition regime by employing the second-order slip boundary conditions. The effects of the second-order slip boundary conditions are analyzed. As in slip and transition regimes, no solutions or graphical and tabulated data exist for most geometries, the developed simple model can be used to predict friction factor, mas
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Reports on the topic "Second order elliptic equation"

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Go Ong, M. E. Hierachical basis preconditioners for second order elliptic problems in three dimensions. Office of Scientific and Technical Information (OSTI), 1989. http://dx.doi.org/10.2172/5005434.

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Manzini, Gianmarco. Annotations on the virtual element method for second-order elliptic problems. Office of Scientific and Technical Information (OSTI), 2017. http://dx.doi.org/10.2172/1338710.

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Messer, Kirsten R. The Second-Order Self-Adjoint Equation With Mixed Derivatives. Defense Technical Information Center, 2002. http://dx.doi.org/10.21236/ada406708.

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Messer, Kirsten R. A Second-Order Self-Adjoint Dynamic Equation on a Time Scale. Defense Technical Information Center, 2002. http://dx.doi.org/10.21236/ada407858.

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Symes, Wiliam W. Trace Regularity for a Second Order Hyperbolic Equation With Nonsmooth Coefficients. Defense Technical Information Center, 1991. http://dx.doi.org/10.21236/ada452695.

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Heningburg, Vincent. Hybrid Discrete Ordinates Solver for the Radiative Transport Equation using Second Order Finite Volume and Discontinuous Galerkin. Office of Scientific and Technical Information (OSTI), 2018. http://dx.doi.org/10.2172/1467230.

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Carroll, Christopher. Death to the Log-Linearized Consumption Euler Equation! (And Very Poor Health to the Second-Order Approximation). National Bureau of Economic Research, 1997. http://dx.doi.org/10.3386/w6298.

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Mamedov, Khanlar R. On a Basic Problem for a Second Order Differential Equation With a Discontinuous Coefficient and a Spectral Parameter in the Boundary Conditions. GIQ, 2012. http://dx.doi.org/10.7546/giq-7-2006-218-225.

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Trahan, Corey, Jing-Ru Cheng, and Amanda Hines. ERDC-PT : a multidimensional particle tracking model. Engineer Research and Development Center (U.S.), 2023. http://dx.doi.org/10.21079/11681/48057.

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This report describes the technical engine details of the particle- and species-tracking software ERDC-PT. The development of ERDC-PT leveraged a legacy ERDC tracking model, “PT123,” developed by a civil works basic research project titled “Efficient Resolution of Complex Transport Phenomena Using Eulerian-Lagrangian Techniques” and in part by the System-Wide Water Resources Program. Given hydrodynamic velocities, ERDC-PT can track thousands of massless particles on 2D and 3D unstructured or converted structured meshes through distributed processing. At the time of this report, ERDC-PT support
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Bailey Bond, Robert, Pu Ren, James Fong, Hao Sun, and Jerome F. Hajjar. Physics-informed Machine Learning Framework for Seismic Fragility Analysis of Steel Structures. Northeastern University, 2024. http://dx.doi.org/10.17760/d20680141.

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The seismic assessment of structures is a critical step to increase community resilience under earthquake hazards. This research aims to develop a Physics-reinforced Machine Learning (PrML) paradigm for metamodeling of nonlinear structures under seismic hazards using artificial intelligence. Structural metamodeling, a reduced-fidelity surrogate model to a more complex structural model, enables more efficient performance-based design and analysis, optimizing structural designs and ease the computational effort for reliability fragility analysis, leading to globally efficient designs while maint
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