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Relevant bibliographies by topics / Geometry of PDEs

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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 (July 2006): 547–66. http://dx.doi.org/10.1016/j.jmaa.2005.06.044.

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

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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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Marsden, Jerrold E., George W. Patrick, and Steve Shkoller. "Multisymplectic Geometry, Variational Integrators, and Nonlinear PDEs." Communications in Mathematical Physics 199, no. 2 (December 1, 1998): 351–95. http://dx.doi.org/10.1007/s002200050505.

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Savin, Ovidiu, and Enrico Valdinoci. "Elliptic PDEs with Fibered Nonlinearities." Journal of Geometric Analysis 19, no. 2 (January 14, 2009): 420–32. http://dx.doi.org/10.1007/s12220-008-9064-5.

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Vitagliano, Luca. "Characteristics, bicharacteristics and geometric singularities of solutions of PDEs." International Journal of Geometric Methods in Modern Physics 11, no. 09 (October 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, geometric point of view, presenting characteristics within the jet space approach to PDEs. In particular, I will discuss the relationship between characteristics and singularities of solutions and observe that: "wave-fronts are characteristic surfaces and propagate along bicharacteristics". This remark may be understood as a mathematical formulation of the wave/particle duality in optics and/or quantum mechanics. The content of the paper reflects the three-hour mini-course that I gave at the XXII International Fall Workshop on Geometry and Physics, September 2–5, 2013, Évora, Portugal.

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Krantz, Steven G., and Vicentiu D. Radulescu. "Perspectives of Geometric Analysis in PDEs." Journal of Geometric Analysis 30, no. 2 (November 1, 2019): 1411. http://dx.doi.org/10.1007/s12220-019-00303-2.

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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 (August 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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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 (June 1, 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 combines ideas of extending surface PDEs to higher-dimensional bulk domains with concepts of trace finite element methods. A particular focus is given to the necessary steps to retain discrete analogues to conservation laws of the discretized PDEs. A high degree of geometric flexibility is achieved by using a level set representation of the geometry. We present theoretical results to prove stability of the method and to investigate its conservation properties. Convergence is shown in an energy norm and numerical results show optimal convergence order in bulk/surface H 1 {H^{1}} - and L 2 {L^{2}} -norms.

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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 (June 17, 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 environments include. On the other hand, the students viewed their designs more and focused more on product–user relation in the geometric modeling environment. While the students followed a top-down process and produced less number of topologically different design alternatives with the parametric design tool, they had more goal setting activities and higher number of alternative designs in the geometric modeling environment. Originality/value This study indicates that cognitive behaviors of designers in GMEs and PDEs differ significantly and these differences entail further attention from researchers and educators.

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Dissertations / Theses on the topic "Geometry of PDEs"

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DE, PONTI NICOLÒ. "Optimal transport: entropic regularizations, geometry and diffusion PDEs." Doctoral thesis, Università degli studi di Pavia, 2019. http://hdl.handle.net/11571/1292130.

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Marini, Michele. "Some problems in convex analysis across geometry and PDEs." Doctoral thesis, Scuola Normale Superiore, 2016. http://hdl.handle.net/11384/86213.

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Athanasopoulos, Michael, Hassan Ugail, and Castro Gabriela Gonzalez. "Parametric design of aircraft geometry using partial differential equations." Elsevier, 2009. http://hdl.handle.net/10454/2725.

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Ugail, Hassan. "Time-dependent shape parameterisation of complex geometry using PDE surfaces." Nashboro Press, 2004. http://hdl.handle.net/10454/2686.

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Yang, Weiye. "Stochastic analysis and stochastic PDEs on fractals." Thesis, University of Oxford, 2018. http://ora.ox.ac.uk/objects/uuid:43a7af74-c531-424a-9f3d-4277138affbb.

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Stochastic analysis on fractals is, as one might expect, a subfield of analysis on fractals. An intuitive starting point is to observe that on many fractals, one can define diffusion processes whose law is in some sense invariant with respect to the symmetries and self-similarities of the fractal. These can be interpreted as fractal-valued counterparts of standard Brownian motion on Rd. One can study these diffusions directly, for example by computing heat kernel and hitting time estimates. On the other hand, by associating the infinitesimal generator of the fractal-valued diffusion with the Laplacian on Rd, it is possible to pose stochastic partial differential equations on the fractal such as the stochastic heat equation and stochastic wave equation. In this thesis we investigate a variety of questions concerning the properties of diffusions on fractals and the parabolic and hyperbolic SPDEs associated with them. Key results include an extension of Kolmogorov's continuity theorem to stochastic processes indexed by fractals, and existence and uniqueness of solutions to parabolic SPDEs on fractals with Lipschitz data.

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Li, Siran. "Analysis of several non-linear PDEs in fluid mechanics and differential geometry." Thesis, University of Oxford, 2017. https://ora.ox.ac.uk/objects/uuid:20866cbb-e5ab-4a6b-b9dc-88a247d15572.

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In the thesis we investigate two problems on Partial Differential Equations (PDEs) in differential geometry and fluid mechanics. First, we prove the weak L^p continuity of the Gauss-Codazzi-Ricci (GCR) equations, which serve as a compatibility condition for the isometric immersions of Riemannian and semi-Riemannian manifolds. Our arguments, based on the generalised compensated compactness theorems established via functional and micro-local analytic methods, are intrinsic and global. Second, we prove the vanishing viscosity limit of an incompressible fluid in three-dimensional smooth, curved domains, with the kinematic and Navier boundary conditions. It is shown that the strong solution of the Navier-Stokes equation in H^r+1 (r > 5/2) converges to the strong solution of the Euler equation with the kinematic boundary condition in H^r, as the viscosity tends to zero. For the proof, we derive energy estimates using the special geometric structure of the Navier boundary conditions; in particular, the second fundamental form of the fluid boundary and the vorticity thereon play a crucial role. In these projects we emphasise the linkages between the techniques in differential geometry and mathematical hydrodynamics.

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Ugail, Hassan, M. I. G. Bloor, and M. J. Wilson. "Manipulation of PDE surfaces using an interactively defined parameterisation." Elsevier, 1999. http://hdl.handle.net/10454/2669.

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No
Manipulation of PDE surfaces using a set of interactively defined parameters is considered. The PDE method treats surface design as a boundary-value problem and ensures that surfaces can be defined using an appropriately chosen set of boundary conditions and design parameters. Here we show how the data input to the system, from a user interface such as the mouse of a computer terminal, can be efficiently used to define a set of parameters with which to manipulate the surface interactively in real time.

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Ugail, Hassan, and A. Sourin. "Partial differential equations for function based geometry modelling within visual cyberworlds." IEEE Computer Society, 2008. http://hdl.handle.net/10454/2612.

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We propose the use of Partial Differential Equations (PDEs) for shape modelling within visual cyberworlds. PDEs, especially those that are elliptic in nature, enable surface modelling to be defined as boundary-value problems. Here we show how the PDE based on the Biharmonic equation subject to suitable boundary conditions can be used for shape modelling within visual cyberworlds. We discuss an analytic solution formulation for the Biharmonic equation which allows us to define a function based geometry whereby the resulting geometry can be visualised efficiently at arbitrary levels of shape resolutions. In particular, we discuss how function based PDE surfaces can be readily integrated within VRML and X3D environments

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Mascellani, Giovanni. "Fourth-order geometric flows on manifolds with boundary." Doctoral thesis, Scuola Normale Superiore, 2017. http://hdl.handle.net/11384/85715.

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Elyan, Eyad, and Hassan Ugail. "Reconstruction of 3D human facial images using partial differential equations." Academy Publisher, 2007. http://hdl.handle.net/10454/2644.

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One of the challenging problems in geometric modeling and computer graphics is the construction of realistic human facial geometry. Such geometry are essential for a wide range of applications, such as 3D face recognition, virtual reality applications, facial expression simulation and computer based plastic surgery application. This paper addresses a method for the construction of 3D geometry of human faces based on the use of Elliptic Partial Differential Equations (PDE). Here the geometry corresponding to a human face is treated as a set of surface patches, whereby each surface patch is represented using four boundary curves in the 3-space that formulate the appropriate boundary conditions for the chosen PDE. These boundary curves are extracted automatically using 3D data of human faces obtained using a 3D scanner. The solution of the PDE generates a continuous single surface patch describing the geometry of the original scanned data. In this study, through a number of experimental verifications we have shown the efficiency of the PDE based method for 3D facial surface reconstruction using scan data. In addition to this, we also show that our approach provides an efficient way of facial representation using a small set of parameters that could be utilized for efficient facial data storage and verification purposes.

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Books on the topic "Geometry of PDEs"

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Bahns, Dorothea, Wolfram Bauer, and Ingo Witt, eds. Quantization, PDEs, and Geometry. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-22407-7.

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Geometry of PDEs and mechanics. Singapore: World Scientific, 1996.

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Cabré, Xavier, Antoine Henrot, Daniel Peralta-Salas, Wolfgang Reichel, and Henrik Shahgholian. Geometry of PDEs and Related Problems. Edited by Chiara Bianchini, Antoine Henrot, and Rolando Magnanini. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-95186-7.

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Kycia, Radosław A., Maria Ułan, and Eivind Schneider, eds. Nonlinear PDEs, Their Geometry, and Applications. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-17031-8.

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Barbara, Opozda, Simon Udo 1938-, Wiehe Martin, and Stefan Banach International Mathematical Center., eds. PDEs, submanifolds and affine differential geometry. Warszawa: Polish Academy of Sciences, Institute of Mathematics, 2005.

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Martin, Wiehe, Simon Udo 1938-, Opozda Barbara, and Stefan Banach International Mathematical Center., eds. PDEs, submanifolds, and affine differential geometry. Warszawa: Polish Academy of Sciences, Institute of Mathematics, 2002.

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Wiehe, Martin. PDEs, submanifolds and affine differential geometry. Edited by Stefan Banach International Mathematical Center. Warszawa: Polish Academy of Sciences, Institute of Mathematics, 2005.

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Druet, Olivier. Blow-up theory for elliptic PDEs in Riemannian geometry. Princeton, NJ: Princeton University Press, 2004.

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Olivier·, Druet·. Blow-up theory for elliptic PDEs in Riemannian geometry. Princeton· NJ: Princeton University Press·, 2003.

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Capogna, Luca, Pengfei Guan, Cristian E. Gutiérrez, and Annamaria Montanari. Fully Nonlinear PDEs in Real and Complex Geometry and Optics. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-00942-1.

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Book chapters on the topic "Geometry of PDEs"

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Gursky, Matthew J. "PDEs in Conformal Geometry." In Geometric Analysis and PDEs, 1–33. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-01674-5_1.

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Yang, Paul. "Minimal Surfaces in CR Geometry." In Geometric Analysis and PDEs, 253–73. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-01674-5_6.

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Gramchev, Todor. "Gelfand–Shilov Spaces: Structural Properties and Applications to Pseudodifferential Operators in ℝ n." In Quantization, PDEs, and Geometry, 1–68. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-22407-7_1.

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Engliš, Miroslav. "An Excursion into Berezin–Toeplitz Quantization and Related Topics." In Quantization, PDEs, and Geometry, 69–115. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-22407-7_2.

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Comech, Andrew. "Global Attraction to Solitary Waves." In Quantization, PDEs, and Geometry, 117–52. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-22407-7_3.

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Markina, Irina. "Geodesics in Geometry with Constraints and Applications." In Quantization, PDEs, and Geometry, 153–314. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-22407-7_4.

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Kersten, P., I. S. Krasil′shchik, A. M. Verbovetsky, and R. Vitolo. "Hamiltonian Structures for General PDEs." In Differential Equations - Geometry, Symmetries and Integrability, 187–98. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-00873-3_9.

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Greiner, Peter C. "Sub-Riemannian Geometry and Subelliptic PDEs." In Partial Differential Equations and Mathematical Physics, 105–10. Boston, MA: Birkhäuser Boston, 2003. http://dx.doi.org/10.1007/978-1-4612-0011-6_9.

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Prástaro, Agostino. "The Maslov Index in PDEs Geometry." In Essays in Mathematics and its Applications, 311–59. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-31338-2_13.

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Lychagin, Valentin V. "Contact Geometry, Measurement, and Thermodynamics." In Nonlinear PDEs, Their Geometry, and Applications, 3–52. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-17031-8_1.

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Conference papers on the topic "Geometry of PDEs"

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Oliker, Vladimir I. "On the geometry of convex reflectors." In PDEs, Submanifolds and Affine Differential Geometry. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2002. http://dx.doi.org/10.4064/bc57-0-10.

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Li, H. Z. "Variational problems and PDEs in affine differential geometry." In PDEs, Submanifolds and Affine Differential Geometry. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2005. http://dx.doi.org/10.4064/bc69-0-1.

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Belkhelfa, Mohamed, Franki Dillen, and Jun-ichi Inoguchi. "Surfaces with parallel second fundamental form in Bianchi-Cartan-Vranceanu spaces." In PDEs, Submanifolds and Affine Differential Geometry. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2002. http://dx.doi.org/10.4064/bc57-0-5.

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Djorić, Mirjana, and Masafumi Okumura. "CR submanifolds of maximal CR dimension in complex manifolds." In PDEs, Submanifolds and Affine Differential Geometry. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2002. http://dx.doi.org/10.4064/bc57-0-6.

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Gálvez, J. A., and A. Martínez. "Hypersurfaces with constant curvature in Rn+1." In PDEs, Submanifolds and Affine Differential Geometry. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2002. http://dx.doi.org/10.4064/bc57-0-7.

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Gollek, Hubert. "Natural algebraic representation formulas for curves in C3." In PDEs, Submanifolds and Affine Differential Geometry. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2002. http://dx.doi.org/10.4064/bc57-0-8.

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Musso, Emilio, and Lorenzo Nicolodi. "Darboux transforms of Dupin surfaces." In PDEs, Submanifolds and Affine Differential Geometry. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2002. http://dx.doi.org/10.4064/bc57-0-9.

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Cortés, Vicente. "A holomorphic representation formula for parabolic hyperspheres." In PDEs, Submanifolds and Affine Differential Geometry. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2002. http://dx.doi.org/10.4064/bc57-0-1.

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Simon, Udo, Konrad Voss, Luc Vrancken, and Martin Wiehe. "Surfaces with prescribed Weingarten operator." In PDEs, Submanifolds and Affine Differential Geometry. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2002. http://dx.doi.org/10.4064/bc57-0-11.

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Belkhelfa, Mohamed, Ryszard Deszcz, Małgorzata Głogowska, Marian Hotloś, Dorota Kowalczyk, and Leopold Verstraelen. "On some type of curvature conditions." In PDEs, Submanifolds and Affine Differential Geometry. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2002. http://dx.doi.org/10.4064/bc57-0-12.

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Reports on the topic "Geometry of PDEs"

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Moreno, Giovanni. A Natural Geometric Framework for the Space of Initial Data of Nonlinear PDEs. GIQ, 2012. http://dx.doi.org/10.7546/giq-13-2012-245-257.

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Yau, Stephen S. PDE, Differential Geometric and Algebraic Methods in Nonlinear Filtering. Fort Belvoir, VA: Defense Technical Information Center, January 1993. http://dx.doi.org/10.21236/ada260967.

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Yau, Stephen S. PDE, Differential Geometric and Algebraic Methods for Nonlinear Filtering. Fort Belvoir, VA: Defense Technical Information Center, February 1996. http://dx.doi.org/10.21236/ada310330.

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Tannenbaum, Allen R. Geometric PDE's and Invariants for Problems in Visual Control Tracking and Optimization. Fort Belvoir, VA: Defense Technical Information Center, January 2005. http://dx.doi.org/10.21236/ada428955.

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Yau, Stephen S. T. PDE, Differential Geometric, Algebraic, Wavelet and Parallel Computation Methods in Nonlinear Filtering. Fort Belvoir, VA: Defense Technical Information Center, June 2003. http://dx.doi.org/10.21236/ada415460.

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