First-order partial differential equation

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On the relation of delay equations to first-order hyperbolic partial differential equations [PDF]

ESAIM: Control, Optimisation and Calculus of Variations, 2014
This paper establishes the equivalence between systems described by a single first-order hyperbolic partial differential equation and systems described by integral delay equations. System-theoretic results are provided for both classes of systems (among them converse Lyapunov results).
Miroslav Krstic, Iasson Karafyllis
core +7 more sources

Invariants of first order partial differential equations

Boletim da Sociedade Paranaense de Matemática, 2018
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].
Lizandro Sanchez Challapa
doaj +4 more sources

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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Variational first-order partial differential equations

Journal of Differential Equations, 2003
AbstractGeometrical and variational properties of systems of first-order partial differential equations (PDE) on fibered manifolds are studied. Existence of Lagrangians is shown to be equivalent with the existence of a closed form which is global and unique; an explicit construction of this form is given.
Alžběta Haková, Olga Krupková
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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 linear partial differential equation of the first order [PDF]

Osaka Mathematical Journal, 1953
Kasuga, Takashi
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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]