Relevant bibliographies by topics / Conservation laws (Mathematics) Differential equations

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

Academic literature on the topic 'Conservation laws (Mathematics) Differential equations'

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Published: 4 June 2021
Last updated: 6 February 2022

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Journal articles on the topic "Conservation laws (Mathematics) Differential equations"

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MARSON, ANDREA. "NONCONVEX CONSERVATION LAWS AND ORDINARY DIFFERENTIAL EQUATIONS." Journal of the London Mathematical Society 69, no. 02 (March 29, 2004): 428–40. http://dx.doi.org/10.1112/s0024610703005088.

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Hydon, P. E. "Multisymplectic conservation laws for differential and differential-difference equations." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 461, no. 2058 (April 26, 2005): 1627–37. http://dx.doi.org/10.1098/rspa.2004.1444.

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Many well-known partial differential equations can be written as multisymplectic systems. Such systems have a structural conservation law from which scalar conservation laws can be derived. These conservation laws arise as differential consequences of a 1-form ‘quasi-conservation law’, which is related to Noether's theorem. This paper develops the above framework and uses it to introduce a multisymplectic structure for differential-difference equations. The shallow water equations and the Ablowitz–Ladik equations are used to illustrate the general theory. It is found that conservation of potential vorticity is a differential consequence of two conservation laws; this surprising result and its implications are discussed.
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Khalique, C. M., and F. M. Mahomed. "Conservation laws for equations related to soil water equations." Mathematical Problems in Engineering 2005, no. 1 (2005): 141–50. http://dx.doi.org/10.1155/mpe.2005.141.

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We obtain all nontrivial conservation laws for a class of (2+1) nonlinear evolution partial differential equations which are related to the soil water equations. It is also pointed out that nontrivial conservation laws exist for certain classes of equations which admit point symmetries. Moreover, we associate symmetries with conservation laws for special classes of these equations.
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Benn, I. M. "Conservation laws for divergenceless differential equations." Journal of Physics A: Mathematical and General 25, no. 24 (December 21, 1992): 6723–31. http://dx.doi.org/10.1088/0305-4470/25/24/023.

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Van Brunt, B., D. Pidgeon, M. Vlieg-Hulstman, and W. D. Halford. "Conservation laws for second-order parabolic partial differential equations." ANZIAM Journal 45, no. 3 (January 2004): 333–48. http://dx.doi.org/10.1017/s1446181100013407.

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AbstractConservation laws for partial differential equations can be characterised by an operator, the characteristic and a condition involving the adjoint of the Fréchet derivatives of this operator and the operator defining the partial differential equation. This approach was developed by Anco and Bluman and we exploit it to derive conditions for second-order parabolic partial differential equations to admit conservation laws. We show that such partial differential equations admit conservation laws only if the time derivative appears in one of two ways. The adjoint condition, however, is a biconditional, and we use this to prove necessary and sufficient conditions for a certain class of partial differential equations to admit a conservation law.
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JENSSEN, HELGE KRISTIAN, and IRINA A. KOGAN. "SYSTEMS OF HYPERBOLIC CONSERVATION LAWS WITH PRESCRIBED EIGENCURVES." Journal of Hyperbolic Differential Equations 07, no. 02 (June 2010): 211–54. http://dx.doi.org/10.1142/s021989161000213x.

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We study the problem of constructing systems of hyperbolic conservation laws in one space dimension with prescribed eigencurves, i.e. the eigenvector fields of the Jacobian of the flux are given. We formulate this as a typically overdetermined system of equations for the eigenvalues-to-be. Equivalent formulations in terms of differential and algebraic-differential equations are considered. The resulting equations are then analyzed using appropriate integrability theorems (Frobenius, Darboux and Cartan–Kähler). We give a complete analysis of the possible scenarios, including examples, for systems of three equations. As an application we characterize conservative systems with the same eigencurves as the Euler system for 1-dimensional compressible gas dynamics. The case of general rich systems of any size (i.e. when the given eigenvector fields are pairwise in involution; this includes all systems of two equations) is completely resolved and we consider various examples in this class.
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ANCO, STEPHEN C., and GEORGE BLUMAN. "Direct construction method for conservation laws of partial differential equations Part I: Examples of conservation law classifications." European Journal of Applied Mathematics 13, no. 5 (October 2002): 545–66. http://dx.doi.org/10.1017/s095679250100465x.

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An effective algorithmic method is presented for finding the local conservation laws for partial differential equations with any number of independent and dependent variables. The method does not require the use or existence of a variational principle and reduces the calculation of conservation laws to solving a system of linear determining equations similar to that for finding symmetries. An explicit construction formula is derived which yields a conservation law for each solution of the determining system. In the first of two papers (Part I), examples of nonlinear wave equations are used to exhibit the method. Classification results for conservation laws of these equations are obtained. In a second paper (Part II), a general treatment of the method is given.
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Gandarias, M. L., M. S. Bruzón, and M. Rosa. "Symmetries and Conservation Laws for Some Compacton Equation." Mathematical Problems in Engineering 2015 (2015): 1–6. http://dx.doi.org/10.1155/2015/430823.

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We consider some equations with compacton solutions and nonlinear dispersion from the point of view of Lie classical reductions. The reduced ordinary differential equations are suitable for qualitative analysis and their dynamical behaviour is described. We derive by using the multipliers method some nontrivial conservation laws for these equations.
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Gan, Yani, and Changzheng Qu. "Approximate conservation laws of perturbed partial differential equations." Nonlinear Dynamics 61, no. 1-2 (January 7, 2010): 217–28. http://dx.doi.org/10.1007/s11071-009-9643-4.

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Anderson, Ian M., and Juha Pohjanpelto. "Variational principles for differential equations with symmetries and conservation laws." Mathematische Annalen 301, no. 1 (January 1995): 627–53. http://dx.doi.org/10.1007/bf01446652.

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Dissertations / Theses on the topic "Conservation laws (Mathematics) Differential equations"

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Yong, Darryl H. "Solving boundary-value problems for systems of hyperbolic conservation laws with rapidly varying coefficients /." Thesis, Connect to this title online; UW restricted, 2000. http://hdl.handle.net/1773/6760.

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Moses, Lawrenzo D. "Error Estimates for Entropy Solutions to Scalar Conservation Laws with Continuous Flux Functions." University of Akron / OhioLINK, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=akron1353991101.

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Fogarty, Tiernan. "Finite volume methods for acoustics and elasto-plasticity with damage in a heterogeneous medium /." Thesis, Connect to this title online; UW restricted, 2001. http://hdl.handle.net/1773/6751.

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Silva, Kênio Alexsom de Almeida 1979. "Auto-adjunticidade não-linear e leis de conservação para equações evolutivas sobre superfícies regulares." [s.n.], 2013. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306724.

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Orientador: Yuri Dimitrov Bozhkov
Tese (doutorado) ¿ Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica
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Resumo: Nesta tese estudamos o conceito novo de equações diferenciais não - linearmente auto-adjuntas para duas classes gerais de equações evolutivas de segunda ordem quase lineares. Uma vez que essas equações não provêm de um problema variacional, não podemos obter leis de conservação via o Teorema de Noether. Por isto aplicamos tal conceito e o Novo Teorema sobre Leis de Conservação de Nail H. Ibragimov, o qual possibilita-nos a determinação de leis de conservação para qualquer equação diferencial. Obtivemos em ambas as classes, equações não - linearmente auto-adjuntos e leis de conservação para alguns casos particularmente importantes: a) as equações do fluxo de Ricci geométrico, do fluxo de Ricci 2D, do fluxo de Ricci modificada e a equação do calor não-linear, na primeira classe; b) as equações do fluxo geométrico hiperbólico e do fluxo geométrica hiperbólica modificada, na segunda classe de equações evolutivas
Abstract: In this thesis we study the new concept of nonlinear self-adjoint deferential equations for two general classes of quasilinear 2D second order evolution equations. Since these equations do not come from a variational problem, we cannot obtain conservation laws via the Noether's Theorem. Therefore we apply this concept and the New Conservation Theorem of Nail H. Ibragimov, which enables one to establish the conservation laws for any deferential equation. We obtain in classes, nonlinear self-adjoint equations and conservation laws for important particular cases: a) the Ricci flow geometric equation, Ricci flow 2D equation, the modified Ricci flow equation and the nonlinear heat equation in the first class; b) the hyperbolic geometric flow equation and the modified hyperbolic geometric flow equation in the second class of evolution equations
Doutorado
Matematica Aplicada
Doutor em Matemática Aplicada
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Stevens, Ben. "Short-time structural stability of compressible vortex sheets with surface tension." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:378713da-cd05-4b9a-856d-bee2b0fb47ce.

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The main purpose of this work is to prove short-time structural stability of compressible vortex sheets with surface tension. The main result can be summarised as follows. Assume we start with an initial vortex-sheet configuration which consists of two inviscid fluids with density bounded below flowing smoothly past each other, where a strictly positive fixed coefficient of surface tension produces a surface tension force across the common interface, balanced by the pressure jump. We assume the fluids are modelled by the compressible Euler equations in three space dimensions with a very general equation of state relating the pressure, entropy and density in each fluid such that the sound speed is positive. Then, for a short time, which may depend on the initial configuration, there exists a unique solution of the equations with the same structure, that is, two fluids with density bounded below flowing smoothly past each other, where the surface tension force across the common interface balances the pressure jump. The mathematical approach consists of introducing a carefully chosen artificial viscosity-type regularisation which allows one to linearise the system so as to obtain a collection of transport equations for the entropy, pressure and curl together with a parabolic-type equation for the velocity. We prove a high order energy estimate for the non-linear equations that is independent of the artificial viscosity parameter which allows us to send it to zero. This approach loosely follows that introduced by Shkoller et al in the setting of a compressible liquid-vacuum interface. Although already considered by Shkoller et al, we also make some brief comments on the case of a compressible liquid-vacuum interface, which is obtained from the vortex sheets problem by replacing one of the fluids by vacuum, where it is possible to obtain a structural stability result even without surface tension.
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Sampaio, Júlio César Santos 1983. "Sobre simetrias e a teoria de leis de conservação de Ibragimov." [s.n.], 2015. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307216.

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Orientador: Igor Leite Freire
Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica
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Resumo: Neste trabalho estudamos simetrias de Lie e a teoria de leis de conservação desenvolvida por Ibragimov nos últimos 10 anos. Leis de conservação para várias equações sem Lagrangeanas clássicas foram estabelecidas
Abstract: In this work we study Lie point symmetries and the theory on conservation laws developed by Ibragimov in the last 10 years. Conservation laws for several equations without classical Lagrangians were established
Doutorado
Matematica Aplicada
Doutor em Matemática Aplicada
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Wan, Andy Tak Shik. "Finding conservation laws for partial differential equations." Thesis, University of British Columbia, 2010. http://hdl.handle.net/2429/28135.

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In this thesis, we discuss systematic methods of finding conservation laws for systems of partial differential equations (PDEs). We first review the direct method of finding conservation laws. In order to use the direct method, one first seeks a set of conservation law multipliers so that a linear combination of the PDEs with the multipliers will yield a divergence expression. Once a set of conservation law multipliers is determined, one proceeds to find the fluxes of the conservation law. As the solution to the problem of finding conservation law multipliers is well-understood, in this thesis we focus on constructing the fluxes assuming the knowledge of a set of conservation law multipliers. First, we derive a new method called the flux equation method and show that, in general, fluxes can be found by at most computing a line integral. We show that the homotopy integral formula is a special case of the line integral formula obtained from the flux equations. We also show how the line integral formula can be simplified in the presence of a point symmetry of the PDE system and of the set of conservation law multipliers. By examples, we illustrate that the flux equation method can derive fluxes which would be otherwise difficult to find. We also review existing known methods of finding fluxes and make comparison with the flux equation method.
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Suttie, D. G. "Multipliers : a general method of analysis for conservation laws of differential equations." Thesis, University of Canterbury. Physics, 1987. http://hdl.handle.net/10092/8233.

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Conservation laws are studied using 'multipliers' - functions which produce divergences when they multiply an equation. Multipliers are found for a number of well-known equations including those of interest in nonlinear physics such as the Korteweg-de Vries and Sine-Gordon equations. It is conjectured that multipliers exist for all conservation laws which are valid for all solutions of an equation. The close links between multipliers and other properties of conservation laws are demonstrated and the identity - at least for Hamiltonian systems - of multipliers with the gradients of conservation laws is shown. By using a formula for the variational derivative of a product of two functions some previously known results are obtained in a simple and direct way. It is also found that the equation ut + un + R = 0, R polynomial, has at most one polynomial conservation law (the equation itself) unless n is odd. The concepts of rank and irreducible terms used by Kruskal et al (J. Math. Phys. 11 952) are generalised and are used to provide a completely new framework for the study of conservation laws. This new framework is used to study the conservation laws of equations such as the Korteweg-de Vries equation and to generalise the result earlier obtained for ut + un + R = 0. Recursion operators are studied and it is found that the concepts used in the framework can be used to give the general form that a recursion operator must take. It is shown that the use of multipliers can produce results for systems of more than one equation by demonstrating that the known integrals for the Henon-Heiles system could be found using multipliers. The framework developed can be incorporated in a computer program and a method of using multipliers by means of such a program is given and illustrated.
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Zhang, Zhengru. "Moving mesh methods for convection-dominated equations and nonlinear conservation laws." HKBU Institutional Repository, 2003. http://repository.hkbu.edu.hk/etd_ra/512.

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Choe, Kyu Y. "The discontinuous finite element method with the Taylor-Galerkin approach for nonlinear hyperbolic conservation laws /." Thesis, Connect to this title online; UW restricted, 1991. http://hdl.handle.net/1773/9977.

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Books on the topic "Conservation laws (Mathematics) Differential equations"

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Henrik, Risebro Nils, ed. Front tracking for hyperbolic conservation laws. New York: Springer-Verlag, 2002.

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Numerical methods for conservation laws. 2nd ed. Basel: Birkhäuser Verlag, 1992.

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Numerical methods for conservation laws. Basel: Birkhäuser Verlag, 1990.

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Henrik, Risebro Nils, and SpringerLink (Online service), eds. Front Tracking for Hyperbolic Conservation Laws. Berlin, Heidelberg: Springer-Verlag Berlin Heidelberg, 2011.

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Vinogradov, A. M. Symmetries of Partial Differential Equations: Conservation Laws - Applications - Algorithms. Dordrecht: Springer Netherlands, 1990.

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Hyperbolic conservation laws and the compensated compactness method. Boca Raton: Chapman & Hall/CRC Press Co., 2003.

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Godlewski, Edwige. Numerical approximation of hyperbolic systems of conservation laws. New York: Springer, 1996.

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Nessyahu, Haim. Non-oscillatory central differencing for hyperbolic conservation laws. Hampton, Va: ICASE, 1988.

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Adaptive multiscale schemes for conservation laws. Berlin: Springer, 2003.

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Siegfried, Müller. Adaptive multiscale schemes for conservation laws. Berlin: Springer, 2003.

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Book chapters on the topic "Conservation laws (Mathematics) Differential equations"

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Naz, R., and F. M. Mahomed. "A Note on the Multiplier Approach for Derivation of Conservation Laws for Partial Differential Equations in the Complex Domain." In Springer Proceedings in Mathematics & Statistics, 125–36. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-01376-9_7.

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Ding, Xiaxi, and Tong Zhang. "Nonlinear Hyperbolic Conservation Laws." In Partial Differential Equations in China, 19–29. Dordrecht: Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-011-1198-0_2.

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DiBenedetto, Emmanuele. "Equations of First Order and Conservation Laws." In Partial Differential Equations, 343–410. Boston, MA: Birkhäuser Boston, 1995. http://dx.doi.org/10.1007/978-1-4899-2840-5_8.

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Alinhac, Serge. "Conservation Laws in One-Space Dimension." In Hyperbolic Partial Differential Equations, 41–63. New York, NY: Springer New York, 2009. http://dx.doi.org/10.1007/978-0-387-87823-2_4.

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Meister, Andreas, and Jens Struckmeier. "Hyperbolic Conservation Laws and Industrial Applications." In Hyperbolic Partial Differential Equations, 1–57. Wiesbaden: Vieweg+Teubner Verlag, 2002. http://dx.doi.org/10.1007/978-3-322-80227-9_1.

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Gazizov, Rafail K., Alexey A. Kasatkin, and Stanislav Yu Lukashchuk. "Symmetries, conservation laws and group invariant solutions of fractional PDEs." In Fractional Differential Equations, edited by Anatoly Kochubei and Yuri Luchko, 353–82. Berlin, Boston: De Gruyter, 2019. http://dx.doi.org/10.1515/9783110571660-016.

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Olver, Peter J. "Symmetry Groups and Conservation Laws." In Applications of Lie Groups to Differential Equations, 246–91. New York, NY: Springer US, 1986. http://dx.doi.org/10.1007/978-1-4684-0274-2_4.

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Olver, Peter J. "Symmetry Groups and Conservation Laws." In Applications of Lie Groups to Differential Equations, 242–85. New York, NY: Springer New York, 1993. http://dx.doi.org/10.1007/978-1-4612-4350-2_4.

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Godunov, Sergei K., and Evgenii I. Romenskii. "Differential Equations of Dynamical Processes." In Elements of Continuum Mechanics and Conservation Laws, 121–51. Boston, MA: Springer US, 2003. http://dx.doi.org/10.1007/978-1-4757-5117-8_3.

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Debnath, Lokenath. "Conservation Laws and Shock Waves." In Nonlinear Partial Differential Equations for Scientists and Engineers, 159–83. Boston, MA: Birkhäuser Boston, 1997. http://dx.doi.org/10.1007/978-1-4899-2846-7_5.

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Conference papers on the topic "Conservation laws (Mathematics) Differential equations"

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Botha, B. W., B. du Toit, and P. G. Rousseau. "Development of a Mathematical Compressor Model to Predict Surge in a Closed Loop Brayton Cycle." In ASME Turbo Expo 2003, collocated with the 2003 International Joint Power Generation Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/gt2003-38795.

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The accuracy by which the compressor performance is estimated plays a major role in predicting the transient performance of a gas turbine Brayton cycle. Numerical prediction has proven to be a valuable tool to reduce development costs of such cycles. This document subsequently discusses the expansion of the well-known Greitzer prediction model used for unstable transient compressor operation. The expansion allows for compressibility effects in the compressor as well as integrating the compressor with a turbine in an open cycle. After this it addresses the effect of flow feedback to the compressor inlet due to a closed cycle configuration. From the one-dimensional form of the conservation laws, three partial differential equations are derived governing the dynamics of fluid flow through the compressor. The simulation results for a simple open cycle configuration compares favorably with that published by Greitzer. A similar approach was used for the closed cycle resulting in an oscillation in compressor inlet pressure due to the feedback from the turbine outlet. The study presents a first step into investigating the possibility of including a generic surge and rotating stall model into an existing software code capable of solving complex thermodynamic systems including turbo-machine cycles.
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Hounkonnou, M. N., P. D. Sielenou, Piotr Kielanowski, Victor Buchstaber, Anatol Odzijewicz, Martin Schlichenmaier, and Theodore Voronov. "Conservation Laws for under Determined Systems of Differential Equations." In XXIX WORKSHOP ON GEOMETRIC METHODS IN PHYSICS. AIP, 2010. http://dx.doi.org/10.1063/1.3527428.

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Webb, Gary M., and Stephen C. Anco. "Conservation laws in magnetohydrodynamics and fluid dynamics: Lagrangian approach." In MODERN TREATMENT OF SYMMETRIES, DIFFERENTIAL EQUATIONS AND APPLICATIONS (Symmetry 2019). AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5125089.

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Zhu, Zuo-Nong. "Conservation Laws of Several (2+1)-Dimensional Differential-Difference Hierarchies." In Proceedings of the Twelfth International Conference on Difference Equations and Applications. WORLD SCIENTIFIC, 2010. http://dx.doi.org/10.1142/9789814287654_0035.

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Mhlanga, Isaiah Elvis, and Chaudry Masood Khalique. "Exact solutions and conservation laws for a coupled Benjamin-Bona-Mahony equations." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2017). Author(s), 2018. http://dx.doi.org/10.1063/1.5043850.

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Kaptsov, Evgeniy I., and Sergey V. Meleshko. "Conservation laws of the one-dimensional isentropic gas dynamics equations in Lagrangian coordinates." In MODERN TREATMENT OF SYMMETRIES, DIFFERENTIAL EQUATIONS AND APPLICATIONS (Symmetry 2019). AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5125074.

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Ruggieri, Marianna, and Maria Paola Speciale. "Determination of balance laws for nonautonomous differential equations of s-order." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2016). Author(s), 2017. http://dx.doi.org/10.1063/1.4992677.

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Hussain, Amjad, and Muhammad Asim. "Conservation Laws for Dynamical System Via Generalized Differential Variational Principles of Jourdian and Gauss." In 2018 International Conference on Applied and Engineering Mathematics (ICAEM). IEEE, 2018. http://dx.doi.org/10.1109/icaem.2018.8536266.

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Ruggieri, Marianna, and Maria Paola Speciale. "Construction of balance laws of first order quasilinear systems of partial differential equations." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2016). Author(s), 2017. http://dx.doi.org/10.1063/1.4992676.

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Tanthanuch, Jessada, Evgeniy I. Kaptsov, and Sergey V. Meleshko. "Equation of Rayleigh noise reduction model for medical ultrasound imaging: Symmetry classification and conservation laws in cylindrical coordinates." In MODERN TREATMENT OF SYMMETRIES, DIFFERENTIAL EQUATIONS AND APPLICATIONS (Symmetry 2019). AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5125087.

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