Results 21 to 30 of about 2,184 (136)
Entire Solutions of Cauchy Problem for Parabolic Monge–Ampère Equations
Advanced Nonlinear Studies, 2020 In this paper, we study the Cauchy problem of the parabolic Monge–Ampère ...
Dai Limei, Bao Jiguang
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The connection between the phase problem in optics, focusing of radiation, and the Monge–Kantorovich problem [PDF]
Компьютерная оптика, 2018 We discuss the use of variational principles for solving the phase problem in optics. In this paper, we consider the connection between four fundamental problems: the phase problem in optics, the inverse problem of focusing coherent radiation, the Monge –
Nikolay Kazanskiy +3 more
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Newton Linearization of the Curvature Operator in Structured Grid Generation with Sample Solutions
International Journal of Mathematics and Mathematical Sciences, Volume 2022, Issue 1, 2022., 2022 Elliptic grid generation equations based on the Laplacian operator have the well‐known property of clustering the mesh near convex boundaries and declustering it near concave boundaries. In prior work, a new differential operator was derived and presented to address this issue.
Pat Piperni +2 more
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Convergent semi-Lagrangian methods for the Monge-Ampère equation on unstructured grids [PDF]
, 2017 This paper is concerned with developing and analyzing convergent semi-Lagrangian methods for the fully nonlinear elliptic Monge-Ampère equation on general triangular grids.
Barles G. +3 more
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Degenerate nonlinear parabolic equations with discontinuous diffusion coefficients
Journal of the London Mathematical Society, Volume 104, Issue 2, Page 688-746, September 2021., 2021 Abstract This paper is devoted to the study of some nonlinear parabolic equations with discontinuous diffusion intensities. Such problems appear naturally in physical and biological models. Our analysis is based on variational techniques and in particular on gradient flows in the space of probability measures equipped with the distance arising in the ...
Dohyun Kwon, Alpár Richárd Mészáros
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Fortschritte der Physik, Volume 69, Issue 7, July 2021., 2021 Abstract Determining whether a dynamical system is integrable is generally a difficult task which is currently done on a case by case basis requiring large human input. Here we propose and test an automated method to search for the existence of relevant structures, the Lax pair and Lax connection respectively.
Sven Krippendorf +2 more
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Three ways to solve partial differential equations with neural networks — A review
GAMM-Mitteilungen, Volume 44, Issue 2, June 2021., 2021 Abstract Neural networks are increasingly used to construct numerical solution methods for partial differential equations. In this expository review, we introduce and contrast three important recent approaches attractive in their simplicity and their suitability for high‐dimensional problems: physics‐informed neural networks, methods based on the ...
Jan Blechschmidt, Oliver G. Ernst
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Pracì Mìžnarodnogo Geometričnogo Centru, 2021 We study the relationship between structural properties of the two-dimensional nonconjugate subalgebras of the same rank of the Lie algebra of the Poincaré group P(1,4) and the properties of reduced equations for the (1+3)-dimensional homogeneous Monge ...
Vasyl Fedorchuk, Volodymyr Fedorchuk
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Minimal convex extensions and finite difference discretization of the quadratic Monge-Kantorovich problem [PDF]
, 2018 We present an adaptation of the MA-LBR scheme to the Monge-Amp{\`e}re equation with second boundary value condition, provided the target is a convex set.
Benamou, Jean-David, Duval, Vincent
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The Initial and Neumann Boundary Value Problem for a Class Parabolic Monge-Ampère Equation
Abstract and Applied Analysis, 2013 We consider the existence, uniqueness, and asymptotic behavior of a classical solution to the initial and Neumann boundary value problem for a class nonlinear parabolic equation of Monge-Ampère type. We show that such solution exists for all times and is
Juan Wang, Jinlin Yang, Xinzhi Liu
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