Results 1 to 10 of about 532,574 (93)
Navier--Stokes equations, the algebraic aspect [PDF]
, 2021 Analysis of the Navier-Stokes equations in the frames of the algebraic approach to systems of partial differential equations (formal theory of differential equations) is presented.
arxiv +1 more source
Triviality of differential Galois cohomologies of linear differential algebraic groups [PDF]
Communications in Algebra 47 (2019) 5094-5100, 2017 We show that the triviality of the differential Galois cohomologies over a partial differential field K of a linear differential algebraic group is equivalent to K being algebraically, Picard-Vessiot, and linearly differentially closed. This former is also known to be equivalent to the uniqueness up to an isomorphism of a Picard-Vessiot extension of a ...
arxiv +1 more source
On Integro-Differential Algebras [PDF]
Journal of Pure and Applied Algebra 218 (2014), 456-471, 2012 The concept of integro-differential algebra has been introduced recently in the study of boundary problems of differential equations. We generalize this concept to that of integro-differential algebra with a weight, in analogy to the differential Rota-Baxter algebra. We construct free commutative integro-differential algebras with weight generated by a
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Ordinary differential equations described by their Lie symmetry algebra [PDF]
Published in J. Geom. Phys. 85 (2014), 2-15, 2014 The theory of Lie remarkable equations, i.e. differential equations characterized by their Lie point symmetries, is reviewed and applied to ordinary differential equations. In particular, we consider some relevant Lie algebras of vector fields on $\mathbb{R}^k$ and characterize Lie remarkable equations admitted by the considered Lie algebras.
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On solvability of dissipative partial differential-algebraic equations [PDF]
arXiv, 2022 In this article we investigate the solvability of infinite-dimensional differential algebraic equations. Such equations often arise as partial differential-algebraic equations (PDAEs). A decomposition of the state-space that leads to an extension of the Hille-Yosida Theorem on Hilbert spaces for these equations is described.
arxiv
Questions concerning differential-algebraic operators: Toward a reliable direct numerical treatment of differential-algebraic equations [PDF]
arXiv, 2019 The nature of so-called differential-algebraic operators and their approximations is constitutive for the direct treatment of higher-index differential-algebraic equations. We treat first-order differential-algebraic operators in detail and contribute to justify the overdetermined polynomial collocation applied to higher-index differential-algebraic ...
arxiv
Algebraic entropy for differential-delay equations [PDF]
arXiv, 2014 We extend the definition of algebraic entropy to a class of differential-delay equations. The vanishing of the entropy, as a structural property of an equation, signals its integrability. We suggest a simple way to produce differential-delay equations with vanishing entropy from known integrable differential-difference equations.
arxiv
First order algebraic differential equations of genus zero [PDF]
, 2016 We utilise recent results about the transcendental solutions to Riccati differential equations to provide a comprehensive description of the nature of the transcendental solutions to algebraic first order differential equations of genus zero.
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Differential equations defined on algebraic curves [PDF]
arXiv, 2016 The class of ordinary linear constant coefficient differential equations is naturally embedded into a wider class by associating differential equations to algebraic curves.
arxiv
A Classification of First Order Differential Equations [PDF]
arXiv, 2023 Let $k$ be a differential field of characteristic zero with an algebraically closed field of constants. In this article, we provide a classification of first order differential equations over $k$ and study the algebraic dependence of solutions of a given first order differential equation.
arxiv