Relevant bibliographies by topics / First order partial differential equations

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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 'First order partial differential equations'

Author: Grafiati
Published: 4 June 2021
Last updated: 21 February 2023

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Journal articles on the topic "First order partial differential equations"

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Aris, Rhee, and Amudson. "First-order partial differential equations." Chemical Engineering Science 42, no. 10 (1987): 2493–94. http://dx.doi.org/10.1016/0009-2509(87)80131-8.

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Barták, Jaroslav, and Otto Vejvoda. "Periodic solutions to linear partial differential equations of the first order." Czechoslovak Mathematical Journal 41, no. 2 (1991): 185–202. http://dx.doi.org/10.21136/cmj.1991.102452.

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Haková, Alžběta, and Olga Krupková. "Variational first-order partial differential equations." Journal of Differential Equations 191, no. 1 (June 2003): 67–89. http://dx.doi.org/10.1016/s0022-0396(02)00160-2.

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Droniou, Jérôme, and Cyril Imbert. "Fractal First-Order Partial Differential Equations." Archive for Rational Mechanics and Analysis 182, no. 2 (April 3, 2006): 299–331. http://dx.doi.org/10.1007/s00205-006-0429-2.

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Challapa, Lizandro Sanchez. "Invariants of first order partial differential equations." Boletim da Sociedade Paranaense de Matemática 38, no. 2 (February 19, 2018): 133–45. http://dx.doi.org/10.5269/bspm.v38i2.34388.

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In this paper we introduce the concepts of multiplicity and index of first order partial differential equations. In particular, the concept of multiplicity coincides with the multiplicity of implicit differential equations given by Bruce and Tari in [2]. We also show that these concepts are invariants by smooth equivalences. Following the works Hayakawa, Ishikawa, Izumiya and Yamaguchi on implicit differential equations with first integrals, we introduce a definition of multiplicity for this class of equations
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Hosoya, Yuhki. "First-order partial differential equations and consumer theory." Discrete & Continuous Dynamical Systems - S 11, no. 6 (2018): 1143–67. http://dx.doi.org/10.3934/dcdss.2018065.

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Li, Bao Qin, and Elias G. Saleeby†. "Entire Solutions of First-order Partial Differential Equations." Complex Variables, Theory and Application: An International Journal 48, no. 8 (August 2003): 657–61. http://dx.doi.org/10.1080/0278107031000151329.

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Holmgren, Sverker, and Kurt Otto. "Semicirculant Preconditioners for First-Order Partial Differential Equations." SIAM Journal on Scientific Computing 15, no. 2 (March 1994): 385–407. http://dx.doi.org/10.1137/0915027.

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Turo, Jan. "Stochastic functional partial differential equations of first order." Stochastic Analysis and Applications 14, no. 2 (January 1996): 245–56. http://dx.doi.org/10.1080/07362996608809437.

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Lakhtin, A. S., and A. I. Subbotin. "Multivalued solutions of first-order partial differential equations." Sbornik: Mathematics 189, no. 6 (June 30, 1998): 849–73. http://dx.doi.org/10.1070/sm1998v189n06abeh000323.

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Dissertations / Theses on the topic "First order partial differential equations"

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Park, Elinor Jane. "Regularizations of first order partial differential equations by generators of semigroups." Thesis, Swansea University, 2005. https://cronfa.swan.ac.uk/Record/cronfa42982.

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This thesis investigates the limiting behaviour of solutions to certain partial and pseudo differential equations. Included is a study of the notion of generalised solutions and particular examples, with emphasis on hyperbolic conservation laws. A probabilistic interpretation of some results is also presented.
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Aziz, Waleed. "Analytic and algebraic aspects of integrability for first order partial differential equations." Thesis, University of Plymouth, 2013. http://hdl.handle.net/10026.1/1468.

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This work is devoted to investigating the algebraic and analytic integrability of first order polynomial partial differential equations via an understanding of the well-developed area of local and global integrability of polynomial vector fields. In the view of characteristics method, the search of first integrals of the first order partial differential equations P(x,y,z)∂z(x,y) ∂x +Q(x,y,z)∂z(x,y) ∂y = R(x,y,z), (1) is equivalent to the search of first integrals of the system of the ordinary differential equations dx/dt= P(x,y,z), dy/dt= Q(x,y,z), dz/dt= R(x,y,z). (2) The trajectories of (2) will be found by representing these trajectories as the intersection of level surfaces of first integrals of (1). We would like to investigate the integrability of the partial differential equation (1) around a singularity. This is a case where understanding of ordinary differential equations will help understanding of partial differential equations. Clearly, first integrals of the partial differential equation (1), are first integrals of the ordinary differential equations (2). So, if (2) has two first integrals φ1(x,y,z) =C1and φ2(x,y,z) =C2, where C1and C2 are constants, then the general solution of (1) is F(φ1,φ2) = 0, where F is an arbitrary function of φ1and φ2. We choose for our investigation a system with quadratic nonlinearities and such that the axes planes are invariant for the characteristics: this gives three dimensional Lotka– Volterra systems x' =dx/dt= P = x(λ +ax+by+cz), y' =dy/dt= Q = y(µ +dx+ey+ fz), z' =dz/dt= R = z(ν +gx+hy+kz), where λ,µ,ν 6= 0. v Several problems have been investigated in this work such as the study of local integrability and linearizability of three dimensional Lotka–Volterra equations with (λ:µ:ν)–resonance. More precisely, we give a complete set of necessary and sufficient conditions for both integrability and linearizability for three dimensional Lotka-Volterra systems for (1:−1:1), (2:−1:1) and (1:−2:1)–resonance. To prove their sufficiency, we mainly use the method of Darboux with the existence of inverse Jacobi multipliers, and the linearizability of a node in two variables with power-series arguments in the third variable. Also, more general three dimensional system have been investigated and necessary and sufficient conditions are obtained. In another approach, we also consider the applicability of an entirely different method which based on the monodromy method to prove the sufficiency of integrability of these systems. These investigations, in fact, mean that we generalized the classical centre-focus problem in two dimensional vector fields to three dimensional vector fields. In three dimensions, the possible mechanisms underling integrability are more difficult and computationally much harder. We also give a generalization of Singer’s theorem about the existence of Liouvillian first integrals in codimension 1 foliations in Cnas well as to three dimensional vector fields. Finally, we characterize the centres of the quasi-homogeneous planar polynomial differential systems of degree three. We show that at most one limit cycle can bifurcate from the periodic orbits of a centre of a cubic homogeneous polynomial system using the averaging theory of first order.
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Stanistreet, Timothy Francis. "Numerical methods for first order partial differential equations describing steady-state forming processes." Thesis, Imperial College London, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.398232.

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Jonasson, Jens. "Systems of Linear First Order Partial Differential Equations Admitting a Bilinear Multiplication of Solutions." Doctoral thesis, Linköping : Department of Mathematics, Linköpings universitet, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-9949.

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Studener, Stephan [Verfasser]. "Embedded Control and Parameter Estimation Algorithms for Transport Process Systems : modeled by first-order Partial Differential Equations / Stephan Studener." Aachen : Shaker, 2011. http://d-nb.info/1069049832/34.

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Gorgone, Matteo. "Symmetries, Equivalence and Decoupling of First Order PDE's." Doctoral thesis, Università di Catania, 2017. http://hdl.handle.net/10761/3901.

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The present Ph.D. Thesis is concerned with first order PDE's and to the structural conditions allowing for their transformation into an equivalent, and somehow simpler, form. Most of the results are framed in the context of the classical theory of the Lie symmetries of differential equations, and on the analysis of some invariant quantities. The thesis is organized in 5 main sections. The first two Chapters present the basic elements of the Lie theory and some introductory facts about first order PDE's, with special emphasis on quasilinear ones. Chapter 3 is devoted to investigate equivalence transformations, i.e., point transformations suitable to deal with classes of differential equations involving arbitrary elements. The general framework of equivalence transformations is then applied to a class of systems of first order PDE's, consisting of a linear conservation law and four general balance laws involving some arbitrary continuously differentiable functions, in order to identify the elements of the class that can be mapped to a system of autonomous conservation laws. Chapter 4 is concerned with the transformation of nonlinear first order systems of differential equations to a simpler form. At first, the reduction to an equivalent first order autonomous and homogeneous quasilinear form is considered. A theorem providing necessary conditions is given, and the reduction to quasilinear form is performed by constructing the canonical variables associated to the Lie point symmetries admitted by the nonlinear system. Then, a general nonlinear system of first order PDE's involving the derivatives of the unknown variables in polynomial form is considered, and a theorem giving necessary and sufficient conditions in order to map it to an autonomous system polynomially homogeneous in the derivatives is established. Several classes of first order Monge-Ampere systems, either with constant coefficients or with coefficients depending on the field variables, provided that the coefficients entering their equations satisfy some constraints, are reduced to quasilinear (or linear) form. Chapter 5 faces the decoupling problem of general quasilinear first order systems. Starting from the direct decoupling problem of hyperbolic quasilinear first order systems in two independent variables and two or three dependent variables, we observe that the decoupling conditions can be written in terms of the eigenvalues and eigenvectors of the coefficient matrix. This allows to obtain a completely general result. At first, general autonomous and homogeneous quasilinear first order systems (either hyperbolic or not) are discussed, and the necessary and sufficient conditions for the decoupling in two or more subsystems proved. Then, the analysis is extended to the case of nonhomogeneous and/or nonautonomous systems. The conditions, as one expects, involve just the properties of the eigenvalues and the eigenvectors (together with the generalized eigenvectors, if needed) of the coefficient matrix; in particular, the conditions for the full decoupling of a hyperbolic system in non-interacting subsystems have a physical interpretation since require the vanishing both of the change of characteristic speeds of a subsystem across a wave of the other subsystems, and of the interaction coefficients between waves of different subsystems. Moreover, when the required decoupling conditions are satisfied, we have also the differential constraints whose integration provides the variable transformation leading to the (partially or fully) decoupled system. All the results are extended to the decoupling of nonhomogeneous and/or nonautonomous quasilinear first order systems.
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Strogies, Nikolai. "Optimization of nonsmooth first order hyperbolic systems." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät, 2016. http://dx.doi.org/10.18452/17633.

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Wir betrachten Optimalsteuerungsprobleme, die von partiellen Differentialgleichungen beziehungsweise Variationsungleichungen mit Differentialoperatoren erster Ordnung abhängen. Wir führen die Reformulierung eines Tagebauplanungsproblems, das auf stetigen Funktionen beruht, ein. Das Resultat ist ein Optimalsteuerungsproblem für Viskositätslösungen einer Eikonalgleichung. Die Existenz von Lösungen dieses und bestimmter Hilfsprobleme, die von semilinearen PDG‘s mit künstlicher Viskosität abhängen, wird bewiesen, Stationaritätsbedingungen hergeleitet und ein schwaches Konsistenzresultat für stationäre Punkte präsentiert. Des Weiteren betrachten wir Optimalsteuerungsprobleme, die von stationären Variationsungleichungen erster Art mit linearen Differentialoperatoren erster Ordnung abhängen. Wir diskutieren Lösbarkeit und Stationaritätskonzepte für diese Probleme. Für letzteres vergleichen wir Ergebnisse, die entweder durch die Anwendung von Penalisierungs- und Regularisierungsansätzen direkt auf Ebene von Differentialoperatoren erster Ordnung oder als Grenzwertprozess von Stationaritätssystemen für viskositätsregularisierte Optimalsteuerungsprobleme unter passenden Annahmen erhalten werden. Um die Konsistenz von ursprünglichem und regularisierten Problemen zu sichern, wird ein bekanntes Ergebnis für Lösungen von VU’s mit degeneriertem Differentialoperator erweitert. In beiden Fällen ist die erhaltene Stationarität schwächer als W-stationarität. Die theoretischen Ergebnisse werden anhand numerischer Beispiele verifiziert. Wir erweitern diese Ergebnisse auf Optimalsteuerungsprobleme bezüglich zeitabhängiger VU’s mit Differentialoperatoren erster Ordnung. Hierfür wird die Existenz von Lösungen bewiesen und erneut ein Stationaritätssystem mit Hilfe verschwindender Viskositäten unter bestimmten Beschränktheitsannahmen hergeleitet. Die erhaltenen Ergebnisse werden anhand von numerischen Beispielen verifiziert.
We consider problems of optimal control subject to partial differential equations and variational inequality problems with first order differential operators. We introduce a reformulation of an open pit mine planning problem that is based on continuous functions. The resulting formulation is a problem of optimal control subject to viscosity solutions of a partial differential equation of Eikonal Type. The existence of solutions to this problem and auxiliary problems of optimal control subject to regularized, semilinear PDE’s with artificial viscosity is proven. For the latter a first order optimality condition is established and a mild consistency result for the stationary points is proven. Further we study certain problems of optimal control subject to time-independent variational inequalities of the first kind with linear first order differential operators. We discuss solvability and stationarity concepts for such problems. In the latter case, we compare the results obtained by either utilizing penalization-regularization strategies directly on the first order level or considering the limit of systems for viscosity-regularized problems under suitable assumptions. To guarantee the consistency of the original and viscosity-regularized problems of optimal control, we extend known results for solutions to variational inequalities with degenerated differential operators. In both cases, the resulting stationarity concepts are weaker than W-stationarity. We validate the theoretical findings by numerical experiments for several examples. Finally, we extend the results from the time-independent to the case of problems of optimal control subject to VI’s with linear first order differential operators that are time-dependent. After establishing the existence of solutions to the problem of optimal control, a stationarity system is derived by a vanishing viscosity approach under certain boundedness assumptions and the theoretical findings are validated by numerical experiments.
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Schnücke, Gero [Verfasser], Christian [Gutachter] Klingenberg, and Manfred [Gutachter] Dobrowolski. "Arbitrary Lagrangian-Eulerian Discontinous Galerkin methods for nonlinear time-dependent first order partial differential equations / Gero Schnücke ; Gutachter: Christian Klingenberg, Manfred Dobrowolski." Würzburg : Universität Würzburg, 2016. http://d-nb.info/1117477290/34.

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Ježková, Jitka. "Modelování dopravního toku." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2015. http://www.nusl.cz/ntk/nusl-232180.

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Tato diplomová práce prezentuje problematiku dopravního toku a jeho modelování. Zabývá se především několika LWR modely, které následně rozebírá a hledá řešení pro počáteční úlohy. Ukazuje se, že ne pro všechny počáteční úlohy lze řešení definovat na celém prostoru, ale jen v určitém okolí počáteční křivky. Proto je dále odvozena metoda výpočtu velikosti tohoto okolí a to nejen zcela obecně, ale i pro dané modely. Teoretický rozbor LWR modelů a řešení počátečních úloh jsou demonstrovány několika příklady, které zřetelně ukazují, jak se dopravní tok simulovaný danými modely chová.
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Shu, Yupeng. "Numerical Solutions of Generalized Burgers' Equations for Some Incompressible Non-Newtonian Fluids." ScholarWorks@UNO, 2015. http://scholarworks.uno.edu/td/2051.

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The author presents some generalized Burgers' equations for incompressible and isothermal flow of viscous non-Newtonian fluids based on the Cross model, the Carreau model, and the Power-Law model and some simple assumptions on the flows. The author numerically solves the traveling wave equations for the Cross model, the Carreau model, the Power-Law model by using industrial data. The author proves existence and uniqueness of solutions to the traveling wave equations of each of the three models. The author also provides numerical estimates of the shock thickness as well as maximum strain $\varepsilon_{11}$ for each of the fluids.
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Books on the topic "First order partial differential equations"

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Rutherford, Aris, and Amundson Neal Russell 1916-, eds. First-order partial differential equations. Englewood Cliffs, N.J: Prentice-Hall, 1986.

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Rhee, Hyun-Ku. First-order partial differential equations. Mineola, N.Y: Dover Publications, 2001.

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F, Zaĭt͡sev V., and Moussiaux Alain, eds. Handbook of first order partial differential equations. London: Taylor & Francis, 2002.

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D, Serre, ed. Multidimensional hyperbolic partial differential equations: First-order systems and applications. Oxford: Clarendon Press, 2007.

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Subbotin, A. I. Generalized solutions of first-order PDEs: The dynamical optimization perspective. Boston: Birkhäuser, 1995.

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Melikyan, A. A. Generalized characteristics of first order PDEs: Applications in optimal control and differential games. Boston: Birhäuser, 1998.

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Tsuji, Mikio. Propagation of singularities for partial differential equations of first order. Recife, Brasil: Universidade Federal de Pernambuco, Centro de Ciências Exatas e da Natureza, Departamento de Matemática, 1989.

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On first and second order planar elliptic equations with degeneracies. Providence, R.I: American Mathematical Society, 2011.

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Van, Tran Duc. The characteristic method and its generalizations for first-order nonlinear partial differential equations. Boca Raton, FL: Chapman & Hall/CRC, 2000.

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Partial differential equations of first order and their applications to physics. Singapore: World Scientific, 1999.

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Book chapters on the topic "First order partial differential equations"

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Kevorkian, J. "Quasilinear First-Order Equations." In Partial Differential Equations, 261–321. Boston, MA: Springer US, 1990. http://dx.doi.org/10.1007/978-1-4684-9022-0_5.

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Kevorkian, J. "Nonlinear First-Order Equations." In Partial Differential Equations, 322–85. Boston, MA: Springer US, 1990. http://dx.doi.org/10.1007/978-1-4684-9022-0_6.

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Dezin, Aleksei A. "First-Order Operator Equations." In Partial Differential Equations, 81–104. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/978-3-642-71334-7_5.

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Dacorogna, Bernard, and Paolo Marcellini. "First Order Equations." In Implicit Partial Differential Equations, 33–68. Boston, MA: Birkhäuser Boston, 1999. http://dx.doi.org/10.1007/978-1-4612-1562-2_2.

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Tikhonov, Andrei N., Adelaida B. Vasil’eva, and Alexei G. Sveshnikov. "First Order Partial Differential Equations." In Differential Equations, 214–35. Berlin, Heidelberg: Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/978-3-642-82175-2_8.

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Bleecker, David, and George Csordas. "First — Order PDEs." In Basic Partial Differential Equations, 57–120. Boston, MA: Springer US, 1992. http://dx.doi.org/10.1007/978-1-4684-1434-9_2.

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DiBenedetto, Emmanuele. "Quasi-Linear Equations of First-Order." In Partial Differential Equations, 225–63. Boston: Birkhäuser Boston, 2009. http://dx.doi.org/10.1007/978-0-8176-4552-6_8.

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DiBenedetto, Emmanuele. "Non-Linear Equations of First-Order." In Partial Differential Equations, 265–95. Boston: Birkhäuser Boston, 2009. http://dx.doi.org/10.1007/978-0-8176-4552-6_9.

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Epstein, Marcelo. "The Genuinely Nonlinear First-Order Equation." In Partial Differential Equations, 89–112. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-55212-5_5.

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Alinhac, Serge. "Nonlinear First Order Equations." In Hyperbolic Partial Differential Equations, 27–40. New York, NY: Springer New York, 2009. http://dx.doi.org/10.1007/978-0-387-87823-2_3.

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Conference papers on the topic "First order partial differential equations"

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"Characteristic systems of partial differential equations of the first order." In Уфимская осенняя математическая школа - 2022. 2 часть. Baskir State University, 2022. http://dx.doi.org/10.33184/mnkuomsh2t-2022-09-28.56.

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Ponomarev, Anton, Julian Hofmann, and Lutz Gröll. "Characteristics-based Simulink Implementation of First-order Quasilinear Partial Differential Equations." In 10th International Conference on Simulation and Modeling Methodologies, Technologies and Applications. SCITEPRESS - Science and Technology Publications, 2020. http://dx.doi.org/10.5220/0009569001390146.

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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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Uskov, Vladimir Igorevich, and Arina Gennadievna Panteleeva. "SOLUTION OF THE CAUCHY PROBLEM FOR SOME FIRST ORDER PARTIAL INTEGRO-DIFFERENTIAL EQUATIONS." In Современные проблемы математики в прикладных науках. Воронеж: Воронежский государственный лесотехнический университет им. Г.Ф. Морозова, 2022. http://dx.doi.org/10.58168/mpmas2022_108-112.

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Tajima, Shinichi, and Katsusuke Nabeshima. "Computing Grothendieck Point Residues via Solving Holonomic Systems of First Order Partial Differential Equations." In ISSAC '21: International Symposium on Symbolic and Algebraic Computation. New York, NY, USA: ACM, 2021. http://dx.doi.org/10.1145/3452143.3465526.

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Ashyralyev, Allaberen, Necmettin Aggez, and Fatih Hezenci. "Boundary value problem for a third order partial differential equation." In FIRST INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS: ICAAM 2012. AIP, 2012. http://dx.doi.org/10.1063/1.4747657.

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Siranosian, Antranik A., Miroslav Krstic, Andrey Smyshlyaev, and Matt Bement. "Gain Scheduling-Inspired Control for Nonlinear Partial Differential Equations." In ASME 2009 Dynamic Systems and Control Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/dscc2009-2532.

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We present a control design method for nonlinear partial differential equations (PDEs) based on a combination of gain scheduling and backstepping theory for linear PDEs. A benchmark first-order hyperbolic system with a destabilizing in-domain nonlinearity is considered first. For this system a nonlinear feedback law based on gain scheduling is derived explicitly, and a statement of stability is presented for the closed-loop system. Control designs are then presented for a string and shear beam PDE, both with Kelvin-Voigt damping and potentially destabilizing free-end nonlinearities. String and beam simulation results illustrate the merits of the gain scheduling approach over the linearization-based design.
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Caruntu, Dumitru I., Roberto J. Zapata, and Martin W. Knecht. "Reduced Order Model of Nanoelectromechanical Systems to Include Casimir Effect." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-48367.

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This paper deals with electrostatically actuated nanoelectromechanical (NEMS) cantilever resonators. The dynamic behavior is described by a second order partial differential equation. The NEMS cantilever resonator device is actuatedby an AC voltage resulting in a vibrating motion of the cantilever. At nano scale, squeeze film damping, Casimir force, and fringing effects significantly influence the dynamic behavior or the cantilever beam. The second order partial differential equation is solved using the Reduced Order Model (ROM) method. The resulting time dependent second order differential equations system is then transformed into a first order differential equations system. Numerical simulations were conducted using Matlab solver ode15s.
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Bazylevych, Yu, and I. Kostiushko. "Matrices diagonalization in solution of partial differential equation of the first order." In APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 11th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS’19. AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5130806.

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Ashyralyev, Allaberen, Sueda Nur Tekalan, and Abdullah Said Erdogan. "On a first order partial differential equation with the nonlocal boundary condition." In INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2014). AIP Publishing LLC, 2014. http://dx.doi.org/10.1063/1.4893862.

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Reports on the topic "First order partial differential equations"

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Cornea, Emil, Ralph Howard, and Per-Gunnar Martinsson. Solutions Near Singular Points to the Eikonal and Related First Order Non-linear Partial Differential Equations in Two Independent Variables. Fort Belvoir, VA: Defense Technical Information Center, March 2000. http://dx.doi.org/10.21236/ada640692.

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Greer, John B., Andrea L. Bertozzi, and Guillermo Sapiro. Fourth Order Partial Differential Equations on General Geometries. Fort Belvoir, VA: Defense Technical Information Center, March 2005. http://dx.doi.org/10.21236/ada524786.

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3

Lathrop, J. F. An implicit integration scheme for first order differential equations. Office of Scientific and Technical Information (OSTI), December 1990. http://dx.doi.org/10.2172/6376877.

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4

Gottlieb, Sigal. High Order Strong Stability Preserving Time Discretizations for the Time Evolution of Hyperbolic Partial Differential Equations. Fort Belvoir, VA: Defense Technical Information Center, February 2012. http://dx.doi.org/10.21236/ada564549.

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5

Mitchell, Jason W. Implementing Families of Implicit Chebyshev Methods with Exact Coefficients for the Numerical Integration of First- and Second-Order Differential Equations. Fort Belvoir, VA: Defense Technical Information Center, May 2002. http://dx.doi.org/10.21236/ada404958.

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