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Relevant bibliographies by topics / Geometry of PDEs

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Journal articles

Academic literature on the topic 'Geometry of PDEs'

Author: Grafiati

Published: 10 March 2023

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Journal articles on the topic "Geometry of PDEs"

1

Prástaro, Agostino. "Geometry of PDEs." Journal of Mathematical Analysis and Applications 319, no. 2 (2006): 547–66. http://dx.doi.org/10.1016/j.jmaa.2005.06.044.

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2

Pràstaro, Agostino. "Quantum geometry of super PDEs." Reports on Mathematical Physics 37, no. 1 (1996): 23–140. http://dx.doi.org/10.1016/0034-4877(96)88921-x.

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3

Gutt, Jan, Gianni Manno, and Giovanni Moreno. "Geometry of Lagrangian Grassmannians and nonlinear PDEs." Banach Center Publications 117 (2019): 9–44. http://dx.doi.org/10.4064/bc117-1.

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4

Marsden, Jerrold E., George W. Patrick, and Steve Shkoller. "Multisymplectic Geometry, Variational Integrators, and Nonlinear PDEs." Communications in Mathematical Physics 199, no. 2 (1998): 351–95. http://dx.doi.org/10.1007/s002200050505.

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5

Savin, Ovidiu, and Enrico Valdinoci. "Elliptic PDEs with Fibered Nonlinearities." Journal of Geometric Analysis 19, no. 2 (2009): 420–32. http://dx.doi.org/10.1007/s12220-008-9064-5.

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6

Vitagliano, Luca. "Characteristics, bicharacteristics and geometric singularities of solutions of PDEs." International Journal of Geometric Methods in Modern Physics 11, no. 09 (2014): 1460039. http://dx.doi.org/10.1142/s0219887814600391.

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Many physical systems are described by partial differential equations (PDEs). Determinism then requires the Cauchy problem to be well-posed. Even when the Cauchy problem is well-posed for generic Cauchy data, there may exist characteristic Cauchy data. Characteristics of PDEs play an important role both in Mathematics and in Physics. I will review the theory of characteristics and bicharacteristics of PDEs, with a special emphasis on intrinsic aspects, i.e. those aspects which are invariant under general changes of coordinates. After a basically analytic introduction, I will pass to a modern,

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7

Krantz, Steven G., and Vicentiu D. Radulescu. "Perspectives of Geometric Analysis in PDEs." Journal of Geometric Analysis 30, no. 2 (2019): 1411. http://dx.doi.org/10.1007/s12220-019-00303-2.

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8

Vinogradov, A. M. "Some remarks on contact manifolds, Monge–Ampère equations and solution singularities." International Journal of Geometric Methods in Modern Physics 11, no. 07 (2014): 1460026. http://dx.doi.org/10.1142/s0219887814600263.

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We describe some natural relations connecting contact geometry, classical Monge–Ampère equations (MAEs) and theory of singularities of solutions to nonlinear PDEs. They reveal the hidden meaning of MAEs and sheds new light on some aspects of contact geometry.

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9

Engwer, Christian, and Sebastian Westerheide. "An Unfitted dG Scheme for Coupled Bulk-Surface PDEs on Complex Geometries." Computational Methods in Applied Mathematics 21, no. 3 (2021): 569–91. http://dx.doi.org/10.1515/cmam-2020-0056.

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Abstract The unfitted discontinuous Galerkin (UDG) method allows for conservative dG discretizations of partial differential equations (PDEs) based on cut cell meshes. It is hence particularly suitable for solving continuity equations on complex-shaped bulk domains. In this paper based on and extending the PhD thesis of the second author, we show how the method can be transferred to PDEs on curved surfaces. Motivated by a class of biological model problems comprising continuity equations on a static bulk domain and its surface, we propose a new UDG scheme for bulk-surface models. The method co

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10

Tünger, Çetin, and Şule Taşlı Pektaş. "A comparison of the cognitive actions of designers in geometry-based and parametric design environments." Open House International 45, no. 1/2 (2020): 87–101. http://dx.doi.org/10.1108/ohi-04-2020-0008.

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Purpose This paper aims to compare designers’ cognitive behaviors in geometry-based modeling environments (GMEs) and parametric design environments (PDEs). Design/methodology/approach This study used Rhinoceros as the geometric and Grasshopper as the parametric design tool in an experimental setting. Designers’ cognitive behaviors were investigated by using the retrospective protocol analysis method with a content-oriented approach. Findings The results indicated that the participants performed more cognitive actions per minute in the PDE because of the extra algorithmic space that such enviro

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