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

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Published: 4 June 2021
Last updated: 21 February 2023

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1

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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2

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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3

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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4

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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5

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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6

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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7

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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8

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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9

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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10

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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11

Subbotin, A. I. "Minimax solutions of first-order partial differential equations." Russian Mathematical Surveys 51, no. 2 (April 30, 1996): 283–313. http://dx.doi.org/10.1070/rm1996v051n02abeh002773.

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12

Smith, B. R. "First-order partial differential equations in classical dynamics." American Journal of Physics 77, no. 12 (December 2009): 1147–53. http://dx.doi.org/10.1119/1.3223358.

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13

Cheema, T. A., M. S. A. Taj, and E. H. Twizell. "Third-order methods for first-order hyperbolic partial differential equations." Communications in Numerical Methods in Engineering 20, no. 1 (November 4, 2003): 31–41. http://dx.doi.org/10.1002/cnm.650.

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14

Turo, Jan. "On some class of quasilinear hyperbolic systems of partial differential-functional equations of the first order." Czechoslovak Mathematical Journal 36, no. 2 (1986): 185–97. http://dx.doi.org/10.21136/cmj.1986.102083.

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15

Zadorozhniy, V. G., and L. Yu Kabantsova. "On Solution of First-Order Linear Systems of Partial Differential Equations." Contemporary Mathematics. Fundamental Directions 67, no. 3 (December 15, 2021): 549–63. http://dx.doi.org/10.22363/2413-3639-2021-67-3-549-563.

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Explicit formulas for the first-order partial differential equations system solving were obtained. Solution found for the system with initial conditions. Calculation examples establishing statements truth mentioned. Searching for partial differential equations system solution mathematical expectation became more difficult issue as partial differential equations system with random processes coefficients were covered. Gaussian coefficients and uniformly distributed random process cases examples has been reviewed.
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16

Turo, Jan. "Nonlocal problems for first order functional partial differential equations." Annales Polonici Mathematici 72, no. 2 (1999): 99–114. http://dx.doi.org/10.4064/ap-72-2-99-114.

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17

Kamont, Z., and S. Kozieł. "First Order Partial Functional Differential Equations with Unbounded Delay." gmj 10, no. 3 (September 2003): 509–30. http://dx.doi.org/10.1515/gmj.2003.509.

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Abstract The phase space for nonlinear hyperbolic functional differential equations with unbounded delay is constructed. The set of axioms for generalized solutions of initial problems is presented. A theorem on the existence and continuous dependence upon initial data is given. The Cauchy problem is transformed into a system of integral functional equations. The existence of solutions of this system is proved by the method of successive approximations and by using theorems on integral inequalities. Examples of phase spaces are given.
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18

Izumiya, Shyuichi. "Characteristic vector fields for first order partial differential equations." Nonlinear Analysis: Theory, Methods & Applications 32, no. 4 (May 1998): 575–82. http://dx.doi.org/10.1016/s0362-546x(97)00501-4.

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19

Hemmati, Jill E. "Entire solutions of first-order nonlinear partial differential equations." Proceedings of the American Mathematical Society 125, no. 5 (1997): 1483–85. http://dx.doi.org/10.1090/s0002-9939-97-03881-1.

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20

Gasanov, K. K., and Kh T. Guseinova. "Vibrocorrect First-Order Partial Differential Equations with Generalized Inputs." Differential Equations 41, no. 4 (April 2005): 585–87. http://dx.doi.org/10.1007/s10625-005-0192-4.

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21

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 (December 29, 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-Dirichlet problem. This work dedicated to systems of first-order partial differential equations of elliptic and hyperbolic types consisting of four equations with three unknown variables. An explicit solution of the CauchyDirichlet problem is constructed using the method of an exponential – differential operator. Giving a very simple example of the co-solution of the Cauchy problem for a second-order differential equation and the Cauchy problem for systems of first-order hyperbolic differential equations.
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22

Favini, A., A. Lorenzi, and H. Tanabe. "First-Order Regular and Degenerate Identification Differential Problems." Abstract and Applied Analysis 2015 (2015): 1–42. http://dx.doi.org/10.1155/2015/393624.

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We are concerned with both regular and degenerate first-order identification problems related to systems of differential equations of weakly parabolic type in Banach spaces. Several applications to partial differential equations and systems will be given in a subsequent paper to show the fullness of our abstract results.
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23

Myronyk, V. I., and V. V. Mykhaylyuk. "First-order linear partial differential equations in the class of separately differentiable functions." Carpathian Mathematical Publications 5, no. 1 (June 20, 2013): 89–93. http://dx.doi.org/10.15330/cmp.5.1.89-93.

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24

Człapiński, Tomasz. "On the existence of generalized solutions of nonlinear first order partial differential-functional equations in two independent variables." Czechoslovak Mathematical Journal 41, no. 3 (1991): 490–506. http://dx.doi.org/10.21136/cmj.1991.102483.

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25

AOKI, Kenji. "A note on duality of first order partial differential equations." Hokkaido Mathematical Journal 24, no. 1 (February 1995): 127–37. http://dx.doi.org/10.14492/hokmj/1380892539.

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26

Kamont, Z., and J. Newlin-Łukowicz. "Generalized Euler Method for Nonlinear First-Order Partial Differential Equations." Nonlinear Oscillations 6, no. 4 (October 2003): 444–62. http://dx.doi.org/10.1023/b:nono.0000028584.03014.72.

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27

Vatsala, A. S. "Periodic boundary value problem for first order partial differential equations." Applicable Analysis 20, no. 1-2 (July 1985): 107–15. http://dx.doi.org/10.1080/00036818508839563.

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28

Kapikyan, A. K., and V. B. Levenshtam. "First-order partial differential equations with large high-frequency terms." Computational Mathematics and Mathematical Physics 48, no. 11 (November 2008): 2059–76. http://dx.doi.org/10.1134/s0965542508110110.

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29

Kepczynska, A. "Implicit Difference Methods for First-Order Partial Differential Functional Equations." Nonlinear Oscillations 8, no. 2 (April 2005): 198–213. http://dx.doi.org/10.1007/s11072-005-0049-z.

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30

Bainov, Drumi, Zdzis?aw Kamont, and Emil Minchev. "Stability of solutions of first-order impulsive partial differential equations." International Journal of Theoretical Physics 33, no. 6 (June 1994): 1359–70. http://dx.doi.org/10.1007/bf00670798.

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31

Khelifa, S., and Y. Cherruault. "The decomposition method for solving first order partial differential equations." Kybernetes 31, no. 6 (August 2002): 844–71. http://dx.doi.org/10.1108/03684920210432817.

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32

Wolfe, Robert, and Hedley C. Morris. "Chaotic Solutions of Systems of First Order Partial Differential Equations." SIAM Journal on Mathematical Analysis 18, no. 4 (July 1987): 1040–63. http://dx.doi.org/10.1137/0518078.

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33

Pennington, S. V., and M. Berzins. "New NAG library software for first-order partial differential equations." ACM Transactions on Mathematical Software 20, no. 1 (March 1994): 63–99. http://dx.doi.org/10.1145/174603.155272.

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34

Kudryashov, Nick A. "Partial differential equations with solutions having movable first-order singularities." Physics Letters A 169, no. 4 (September 1992): 237–42. http://dx.doi.org/10.1016/0375-9601(92)90451-q.

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35

Kamont, Z. "Finite-difference approximation of first-order partial differential-functional equations." Ukrainian Mathematical Journal 46, no. 8 (August 1994): 1079–92. http://dx.doi.org/10.1007/bf01056169.

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36

Vasilyev, Vladimir, and Yuri Virchenko. "Hyperbolicity of First Order Quasi-Linear Equations." Symmetry 14, no. 5 (May 17, 2022): 1024. http://dx.doi.org/10.3390/sym14051024.

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The theorem about equivalence of the strong hyperbolicity concept and the Friedrichs hyperbolicity concept for partial quasi-linear differential equations of the first order is proved. On the basis of this theorem, the necessary and sufficient conditions of hyperbolicity are found in terms of the matrix of the corresponding linearized first order equations system.
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37

Kandala, Shanti S., Surya Samukham, Thomas K. Uchida, and C. P. Vyasarayani. "Spurious roots of delay differential equations using Galerkin approximations." Journal of Vibration and Control 26, no. 15-16 (January 13, 2020): 1178–84. http://dx.doi.org/10.1177/1077546319894172.

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The dynamics of time-delay systems are governed by delay differential equations, which are infinite dimensional and can pose computational challenges. Several methods have been proposed for studying the stability characteristics of delay differential equations. One such method employs Galerkin approximations to convert delay differential equations into partial differential equations with boundary conditions; the partial differential equations are then converted into systems of ordinary differential equations, whereupon standard ordinary differential equation methods can be applied. The Galerkin approximation method can be applied to a second-order delay differential equation in two ways: either by converting into a second-order partial differential equation and then into a system of second-order ordinary differential equations (the “second-order Galerkin” method) or by first expressing as two first-order delay differential equations and converting into a system of first-order partial differential equations and then into a first-order ordinary differential equation system (the “first-order Galerkin” method). In this paper, we demonstrate that these subtly different formulation procedures lead to different roots of the characteristic polynomial. In particular, the second-order Galerkin method produces spurious roots near the origin, which must then be identified through substitution into the characteristic polynomial of the original delay differential equation. However, spurious roots do not arise if the first-order Galerkin method is used, which can reduce computation time and simplify stability analyses. We describe these two formulation strategies and present numerical examples to highlight their important differences.
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38

Karafyllis, Iasson, and Miroslav Krstic. "On the relation of delay equations to first-order hyperbolic partial differential equations." ESAIM: Control, Optimisation and Calculus of Variations 20, no. 3 (June 13, 2014): 894–923. http://dx.doi.org/10.1051/cocv/2014001.

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39

Gorgone, Matteo, and Francesco Oliveri. "Nonlinear first order partial differential equations reducible to first order homogeneous and autonomous quasilinear ones." Ricerche di Matematica 66, no. 1 (May 2, 2016): 51–63. http://dx.doi.org/10.1007/s11587-016-0286-8.

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40

Cai, Zhiqiang, Thomas A. Manteuffel, and Stephen F. McCormick. "First-Order System Least Squares for Second-Order Partial Differential Equations: Part II." SIAM Journal on Numerical Analysis 34, no. 2 (April 1997): 425–54. http://dx.doi.org/10.1137/s0036142994266066.

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41

Cai, Zhiqiang, Rob Falgout, and Shun Zhang. "Div First-Order System LL* (FOSLL*) for Second-Order Elliptic Partial Differential Equations." SIAM Journal on Numerical Analysis 53, no. 1 (January 2015): 405–20. http://dx.doi.org/10.1137/140971890.

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42

Cai, Z., R. Lazarov, T. A. Manteuffel, and S. F. McCormick. "First-Order System Least Squares for Second-Order Partial Differential Equations: Part I." SIAM Journal on Numerical Analysis 31, no. 6 (December 1994): 1785–99. http://dx.doi.org/10.1137/0731091.

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43

Kuziv, Yaroslav Yu. "Software for the numerical solution of first-order partial differential equations." Discrete and Continuous Models and Applied Computational Science 27, no. 1 (December 15, 2019): 42–48. http://dx.doi.org/10.22363/2658-4670-2019-27-1-42-48.

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Partial differential equations of the first order, arising in applied problems of optics and optoelectronics, often contain coefficients that are not defined by a single analytical expression in the entire considered domain. For example, the eikonal equation contains the refractive index, which is described by various expressions depending on the optical properties of the media that fill the domain under consideration. This type of equations cannot be analysed by standard tools built into modern computer algebra systems, including Maple.The paper deals with the adaptation of the classical Cauchy method of integrating partial differential equations of the first order to the case when the coefficients of the equation are given by various analytical expressions in the subdomains G1, . . . , Gk , into which the considered domain is divided. In this case, it is assumed that these subdomains are specified by inequalities. This integration method is implemented as a Python program using the SymPy library. The characteristics are calculatednumerically using the Runge-Kutta method, but taking into account the change in the expressions for the coefficients of the equation when passing from one subdomain to another. The main functions of the program are described, including those that can be used to illustrate the Cauchy method. The verification was carried out by comparison with the results obtained in the Maple computer algebra system.
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44

Szafrańska, A. "Method of lines for nonlinear first order partial functional differential equations." Bulletin of the Belgian Mathematical Society - Simon Stevin 20, no. 5 (November 2013): 859–80. http://dx.doi.org/10.36045/bbms/1385390769.

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45

Gérard, Raymond, and Hidetoshi Tahara. "Nonlinear singular first order partial differential equations of Briot-Bouquet type." Proceedings of the Japan Academy, Series A, Mathematical Sciences 66, no. 3 (1990): 72–74. http://dx.doi.org/10.3792/pjaa.66.72.

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46

Kamont, Zdzisław, and Adam Nadolski. "GENERALIZED EULER METHOD FOR NONLINEAR FIRST ORDER PARTIAL DIFFERENTIAL FUNCTIONAL EQUATIONS." Demonstratio Mathematica 38, no. 4 (October 1, 2005): 977–96. http://dx.doi.org/10.1515/dema-2005-0423.

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47

Czernous, W. "Generalized method of lines for first order partial functional differential equations." Annales Polonici Mathematici 89, no. 2 (2006): 103–26. http://dx.doi.org/10.4064/ap89-2-1.

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48

Izumiya, Shyūichi, Bing Li, and Jian Ming Yu. "A survey on singular solutions of first-order partial differential equations." Kodai Mathematical Journal 17, no. 3 (1994): 644–49. http://dx.doi.org/10.2996/kmj/1138040058.

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49

Turo, J. "Nonlocal problems for quasilinear functional partial differential equations of first order." Publicacions Matemàtiques 41 (July 1, 1997): 507–17. http://dx.doi.org/10.5565/publmat_41297_15.

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50

Cai, Z., T. A. Manteuffel, S. F. McCormick, and J. Ruge. "First-Order System $\CL\CL^*$ (FOSLL*): Scalar Elliptic Partial Differential Equations." SIAM Journal on Numerical Analysis 39, no. 4 (January 2001): 1418–45. http://dx.doi.org/10.1137/s0036142900388049.

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