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Author : Donald Clayton Spencer
Publisher :
ISBN 13 :
Total Pages : 97 pages
Book Rating : 4.:/5 (667 download)
Download or read book Overdetermined Systems of Linear Partial Differential Equations written by Donald Clayton Spencer and published by . This book was released on 1968 with total page 97 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Michael Eastwood
Publisher : Springer Science & Business Media
ISBN 13 : 0387738312
Total Pages : 565 pages
Book Rating : 4.3/5 (877 download)
Download or read book Symmetries and Overdetermined Systems of Partial Differential Equations written by Michael Eastwood and published by Springer Science & Business Media. This book was released on 2009-04-23 with total page 565 pages. Available in PDF, EPUB and Kindle. Book excerpt: This three-week summer program considered the symmetries preserving various natural geometric structures. There are two parts to the proceedings. The articles in the first part are expository but all contain significant new material. The articles in the second part are concerned with original research. All articles were thoroughly refereed and the range of interrelated work ensures that this will be an extremely useful collection.
Author : Daniel Gray Quillen
Publisher :
ISBN 13 :
Total Pages : 96 pages
Book Rating : 4.:/5 (493 download)
Download or read book Formal Properties of Over-determined Systems of Linear Partial Differential Equations written by Daniel Gray Quillen and published by . This book was released on 1964 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Matthew James Randall
Publisher :
ISBN 13 :
Total Pages : 270 pages
Book Rating : 4.:/5 (953 download)
Download or read book Aspects of Overdetermined Systems of Partial Differential Equations in Projective and Conformal Geometry written by Matthew James Randall and published by . This book was released on 2013 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis discusses aspects of overdetermined systems of partial differential equations (PDEs) in projective and conformal geometry. The first part deals with projective differential geometry. A projective surface is a 2-dimensional smooth manifold equipped with a projective structure i.e. a class of torsion-free affine connections that have the same geodesics as unparameterised curves. Given any projective surface we can ask whether it admits a torsion-free affine connection (in its projective class) that has skew-symmetric Ricci tensor. This is equivalent to solving a particular overdetermined system of semi-linear partial differential equations. It turns out that there are local obstructions to solving the system of PDEs in two dimensions. These obstructions are constructed out of local invariants of the projective structure. We give examples of projective surfaces that admit skew-symmetric Ricci tensor and examples that do not because of nonvanishing obstructions. We relate projective surfaces admitting skew-symmetric Ricci tensor to 3-webs in 2 dimensions. We also give examples of projective structures in higher dimensions that admit skew-symmetric Ricci tensor. The second part of the thesis deals with conformal differential geometry. On Mobius surfaces introduced in [5], we can define an analogous overdetermined system of semi-linear PDEs as in the projective case. This is called the scalar-flat Mobius Einstein-Weyl equation and is conformally invariant. We derive local algebraic constraints for Mobius surfaces to admit a solution to this equation and give local obstructions. These obstructions are similarly constructed out of local conformal invariants of the Mobius structure. Again we provide examples of Mobius surfaces that admit a solution and examples that do not because of non-vanishing obstructions. Finally, we also investigate the conformally Einstein equation on Mobius surfaces and derive obstructions. In contrast to the previous two equations, the conformally Einstein equation is linear.
Author : Hubert Leopold Goldschmidt
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (769 download)
Download or read book Overdetermined Systems of Analytic Partial Differential Equations written by Hubert Leopold Goldschmidt and published by . This book was released on 1967 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : M.A. Shubin
Publisher : Springer
ISBN 13 : 9783642489457
Total Pages : 261 pages
Book Rating : 4.4/5 (894 download)
Download or read book Partial Differential Equations VIII written by M.A. Shubin and published by Springer. This book was released on 2014-10-05 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : M.A. Shubin
Publisher : Springer Science & Business Media
ISBN 13 : 3642489443
Total Pages : 266 pages
Book Rating : 4.6/5 (424 download)
Download or read book Partial Differential Equations VIII written by M.A. Shubin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume of the EMS contains three articles, on linear overdetermined systems of partial differential equations, dissipative Schroedinger operators, and index theorems. Each article presents a comprehensive survey of its subject, discussing fundamental results such as the construction of compatibility operators and complexes for elliptic, parabolic and hyperbolic coercive problems, the method of functional models and the Atiyah-Singer index theorem and its generalisations. Both classical and recent results are explained in detail and illustrated by means of examples.
Author : Hubert Goldschmidt
Publisher :
ISBN 13 :
Total Pages : 121 pages
Book Rating : 4.:/5 (218 download)
Download or read book An Introduction to Overdetermined Systems of Partial Differential Equations written by Hubert Goldschmidt and published by . This book was released on 1986 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : M.A. Shubin
Publisher : Springer
ISBN 13 :
Total Pages : 280 pages
Book Rating : 4.:/5 (318 download)
Download or read book Partial Differential Equations VIII written by M.A. Shubin and published by Springer. This book was released on 1995-12-01 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Hung Son Le
Publisher :
ISBN 13 :
Total Pages : 7 pages
Book Rating : 4.:/5 (354 download)
Download or read book Some Overdetermined Systems of Complex Partial Differential Equations written by Hung Son Le and published by . This book was released on 1990 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Daniel Gray Guillén
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (112 download)
Download or read book Formal Propierties Over-determined System of Linear Partial Differential Equations written by Daniel Gray Guillén and published by . This book was released on 1964 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Sergey V. Meleshko
Publisher : Springer Science & Business Media
ISBN 13 : 0387252657
Total Pages : 367 pages
Book Rating : 4.3/5 (872 download)
Download or read book Methods for Constructing Exact Solutions of Partial Differential Equations written by Sergey V. Meleshko and published by Springer Science & Business Media. This book was released on 2006-06-18 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential equations, especially nonlinear, present the most effective way for describing complex physical processes. Methods for constructing exact solutions of differential equations play an important role in applied mathematics and mechanics. This book aims to provide scientists, engineers and students with an easy-to-follow, but comprehensive, description of the methods for constructing exact solutions of differential equations.
Author :
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (91 download)
Download or read book Partial Differential Equations: Overdetermined systems, dissipative singular Schro dinger operator, index theory written by and published by . This book was released on 1991 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Partial Differential Equations: Overdetermined systems. Dissipative singular Schrödinger operator. Index theory written by and published by . This book was released on 1991 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (91 download)
Download or read book Partial Differential Equations: Overdetermined systems. Dissipative singular Schrödlinger operator. Index theory written by and published by . This book was released on 1991 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Deane Yang
Publisher : American Mathematical Soc.
ISBN 13 : 0821824333
Total Pages : 109 pages
Book Rating : 4.8/5 (218 download)
Download or read book Involutive Hyperbolic Differential Systems written by Deane Yang and published by American Mathematical Soc.. This book was released on 1987 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Cartan-Kähler theorem demonstrates that certain real analytic exterior differential systems--ones which Cartan dubbed "involutive"--admit local real analytic solutions. The proof reduces the system to a set of determined systems of PDE's which are then solved using the Cauchy-Kovalevski theorem. The subtlety in the theorem and in the definition of involutivity lies in checking that the "solution" obtained from the determined systems does in fact satisfy the original differential system.
Author : Michael E. Taylor
Publisher : Springer Nature
ISBN 13 : 303133700X
Total Pages : 706 pages
Book Rating : 4.0/5 (313 download)
Download or read book Partial Differential Equations II written by Michael E. Taylor and published by Springer Nature. This book was released on 2023-12-06 with total page 706 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second in the series of three volumes builds upon the basic theory of linear PDE given in volume 1, and pursues more advanced topics. Analytical tools introduced here include pseudodifferential operators, the functional analysis of self-adjoint operators, and Wiener measure. The book also develops basic differential geometrical concepts, centered about curvature. Topics covered include spectral theory of elliptic differential operators, the theory of scattering of waves by obstacles, index theory for Dirac operators, and Brownian motion and diffusion. The book is targeted at graduate students in mathematics and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis, and complex analysis. The third edition further expands the material by incorporating new theorems and applications throughout the book, and by deepening connections and relating concepts across chapters. It includes new sections on rigid body motion, on probabilistic results related to random walks, on aspects of operator theory related to quantum mechanics, on overdetermined systems, and on the Euler equation for incompressible fluids. The appendices have also been updated with additional results, ranging from weak convergence of measures to the curvature of Kahler manifolds. Michael E. Taylor is a Professor of Mathematics at the University of North Carolina, Chapel Hill, NC. Review of first edition: “These volumes will be read by several generations of readers eager to learn the modern theory of partial differential equations of mathematical physics and the analysis in which this theory is rooted.” (Peter Lax, SIAM review, June 1998)
