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Variational first-order partial differential equations

Journal of Differential Equations, 2003
Let \(\pi_1: J^1 Y\to X\) be the jet prolongation of a fibered manifold \(\pi: Y\to X\). Denoting \((x^i, y^\sigma, y^\sigma_j)\) the local fibered coordinates and \(\omega^\sigma= dy^\sigma- \sum y^\sigma_j dx^j\) the contact forms on \(J^1Y\), the article is devoted to formal algebraic properties of the multiple variational integral \(\int\rho ...
Alžběta Haková, Olga Krupková
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Nonlinear differential equation with first order partial derivatives

Вестник КазНУ. Серия математика, механика, информатика, 2018
The asymptotic behavior of solutions of a nonlinear differential equation with first-order partial derivatives solved with respect to one of the derivatives is investigated.
T. М. Aldibekov, M. M. Aldazharova
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Note on the form of a first-order partial differential equation [PDF]

Bulletin of the American Mathematical Society, 1934
Arthur B. Brown
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On the hyperbolic type differential equation with time involution [PDF]

Қарағанды университетінің хабаршысы. Математика сериясы, 2023
In the present paper, the initial value problem for the hyperbolic type involutory in t second order linear partial differential equation is studied.
A. Ashyralyev, A. Ashyralyyev, B. Abdalmohammed   +2 more
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The characteristic equation for partial differential equations of the first order [PDF]

Colloquium Mathematicum, 1958
A. Pilś
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On global solutions for partial differential equations of first order [PDF]

Bulletin of the American Mathematical Society, 1961
Peter Dombrowski
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Comparison of third-order fractional partial differential equation based on the fractional operators using the explicit finite difference method

Alexandria Engineering Journal, 2023
In this research paper, the third-order fractional partial differential equation (FPDE) in the sense of the Caputo fractional derivative and the Atangana-Baleanu Caputo (ABC) fractional derivative is investigated for the first time. The importance of the
Shorish Omer Abdulla, Sadeq Taha Abdulazeez, Mahmut Modanli   +2 more
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Maillet type theorem for singular first order nonlinear partial differential equations of totally characteristic type. Part II [PDF]

Opuscula Mathematica, 2015
In this paper, we study the following nonlinear first order partial differential equation: \[f(t,x,u,\partial_t u,\partial_x u)=0\quad\text{with}\quad u(0,x)\equiv 0.\] The purpose of this paper is to determine the estimate of Gevrey order under the ...
Akira Shirai
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The Z5 transformation for solving quasi-linear partial differential equations

Partial Differential Equations in Applied Mathematics, 2023
The Z1-Z4 transformations proposed in our previous papers have acquired remarkable success in the field of linear partial differential equations, general solutions of a large number of typical equations were obtained for the first time, and exact ...
Hong Lai Zhu
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The Cauchy Problem for First Order Partial Differential Equations [PDF]

Indiana University Mathematics Journal, 1973
Avner Friedman
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