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Elliptic And Parabolic Methods In Geometry
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Book Synopsis Elliptic and Parabolic Methods in Geometry by : Ben Chow
Download or read book Elliptic and Parabolic Methods in Geometry written by Ben Chow and published by CRC Press. This book was released on 1996-10-15 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book documents the results of a workshop held at the Geometry Center (University of Minnesota, Minneapolis) and captures the excitement of the week.
Book Synopsis Geometric Properties for Parabolic and Elliptic PDE's by : Vincenzo Ferone
Download or read book Geometric Properties for Parabolic and Elliptic PDE's written by Vincenzo Ferone and published by Springer Nature. This book was released on 2021-06-12 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the contributions resulting from the 6th Italian-Japanese workshop on Geometric Properties for Parabolic and Elliptic PDEs, which was held in Cortona (Italy) during the week of May 20–24, 2019. This book will be of great interest for the mathematical community and in particular for researchers studying parabolic and elliptic PDEs. It covers many different fields of current research as follows: convexity of solutions to PDEs, qualitative properties of solutions to parabolic equations, overdetermined problems, inverse problems, Brunn-Minkowski inequalities, Sobolev inequalities, and isoperimetric inequalities.
Book Synopsis Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations by : Beatrice Riviere
Download or read book Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations written by Beatrice Riviere and published by SIAM. This book was released on 2008-12-18 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focuses on three primal DG methods, covering both theory and computation, and providing the basic tools for analysis.
Book Synopsis Numerical Methods for Elliptic and Parabolic Partial Differential Equations by : Peter Knabner
Download or read book Numerical Methods for Elliptic and Parabolic Partial Differential Equations written by Peter Knabner and published by Springer Science & Business Media. This book was released on 2003-06-26 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text provides an application oriented introduction to the numerical methods for partial differential equations. It covers finite difference, finite element, and finite volume methods, interweaving theory and applications throughout. The book examines modern topics such as adaptive methods, multilevel methods, and methods for convection-dominated problems and includes detailed illustrations and extensive exercises.
Book Synopsis Elliptic–Hyperbolic Partial Differential Equations by : Thomas H. Otway
Download or read book Elliptic–Hyperbolic Partial Differential Equations written by Thomas H. Otway and published by Springer. This book was released on 2015-07-08 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is a concise introduction to the partial differential equations which change from elliptic to hyperbolic type across a smooth hypersurface of their domain. These are becoming increasingly important in diverse sub-fields of both applied mathematics and engineering, for example: • The heating of fusion plasmas by electromagnetic waves • The behaviour of light near a caustic • Extremal surfaces in the space of special relativity • The formation of rapids; transonic and multiphase fluid flow • The dynamics of certain models for elastic structures • The shape of industrial surfaces such as windshields and airfoils • Pathologies of traffic flow • Harmonic fields in extended projective space They also arise in models for the early universe, for cosmic acceleration, and for possible violation of causality in the interiors of certain compact stars. Within the past 25 years, they have become central to the isometric embedding of Riemannian manifolds and the prescription of Gauss curvature for surfaces: topics in pure mathematics which themselves have important applications. Elliptic−Hyperbolic Partial Differential Equations is derived from a mini-course given at the ICMS Workshop on Differential Geometry and Continuum Mechanics held in Edinburgh, Scotland in June 2013. The focus on geometry in that meeting is reflected in these notes, along with the focus on quasilinear equations. In the spirit of the ICMS workshop, this course is addressed both to applied mathematicians and to mathematically-oriented engineers. The emphasis is on very recent applications and methods, the majority of which have not previously appeared in book form.
Book Synopsis Methods Of Geometry In The Theory Of Partial Differential Equations: Principle Of The Cancellation Of Singularities by : Takashi Suzuki
Download or read book Methods Of Geometry In The Theory Of Partial Differential Equations: Principle Of The Cancellation Of Singularities written by Takashi Suzuki and published by World Scientific. This book was released on 2024-01-22 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical models are used to describe the essence of the real world, and their analysis induces new predictions filled with unexpected phenomena.In spite of a huge number of insights derived from a variety of scientific fields in these five hundred years of the theory of differential equations, and its extensive developments in these one hundred years, several principles that ensure these successes are discovered very recently.This monograph focuses on one of them: cancellation of singularities derived from interactions of multiple species, which is described by the language of geometry, in particular, that of global analysis.Five objects of inquiry, scattered across different disciplines, are selected in this monograph: evolution of geometric quantities, models of multi-species in biology, interface vanishing of d - δ systems, the fundamental equation of electro-magnetic theory, and free boundaries arising in engineering.The relaxation of internal tensions in these systems, however, is described commonly by differential forms, and the reader will be convinced of further applications of this principle to other areas.
Book Synopsis Geometric Methods in PDE’s by : Giovanna Citti
Download or read book Geometric Methods in PDE’s written by Giovanna Citti and published by Springer. This book was released on 2015-10-31 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: The analysis of PDEs is a prominent discipline in mathematics research, both in terms of its theoretical aspects and its relevance in applications. In recent years, the geometric properties of linear and nonlinear second order PDEs of elliptic and parabolic type have been extensively studied by many outstanding researchers. This book collects contributions from a selected group of leading experts who took part in the INdAM meeting "Geometric methods in PDEs", on the occasion of the 70th birthday of Ermanno Lanconelli. They describe a number of new achievements and/or the state of the art in their discipline of research, providing readers an overview of recent progress and future research trends in PDEs. In particular, the volume collects significant results for sub-elliptic equations, potential theory and diffusion equations, with an emphasis on comparing different methodologies and on their implications for theory and applications.
Book Synopsis Elliptic And Parabolic Problems, Proceedings Of The 4th European Conference by : Josef Bemelmans
Download or read book Elliptic And Parabolic Problems, Proceedings Of The 4th European Conference written by Josef Bemelmans and published by World Scientific. This book was released on 2002-08-06 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an overview of the state of the art in important subjects, including — besides elliptic and parabolic issues — geometry, free boundary problems, fluid mechanics, evolution problems in general, calculus of variations, homogenization, control, modeling and numerical analysis.
Book Synopsis Elliptic & Parabolic Equations by : Zhuoqun Wu
Download or read book Elliptic & Parabolic Equations written by Zhuoqun Wu and published by World Scientific. This book was released on 2006 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to elliptic and parabolic equations. While there are numerous monographs focusing separately on each kind of equations, there are very few books treating these two kinds of equations in combination. This book presents the related basic theories and methods to enable readers to appreciate the commonalities between these two kinds of equations as well as contrast the similarities and differences between them.
Book Synopsis Lectures on Elliptic and Parabolic Equations in Holder Spaces by : Nikolaĭ Vladimirovich Krylov
Download or read book Lectures on Elliptic and Parabolic Equations in Holder Spaces written by Nikolaĭ Vladimirovich Krylov and published by American Mathematical Soc.. This book was released on 1996 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lectures concentrate on fundamentals of the modern theory of linear elliptic and parabolic equations in H older spaces. Krylov shows that this theory - including some issues of the theory of nonlinear equations - is based on some general and extremely powerful ideas and some simple computations. The main object of study is the first boundary-value problems for elliptic and parabolic equations, with some guidelines concerning other boundary-value problems such as the Neumann or oblique derivative problems or problems involving higher-order elliptic operators acting on the boundary. Numerical approximations are also discussed. This book, containing 200 exercises, aims to provide a good understanding of what kind of results are available and what kinds of techniques are used to obtain them.
Book Synopsis Multiscale and Geometric Methods for Linear Elliptic and Parabolic Partial Differential Equations by : Shaowu Tang
Download or read book Multiscale and Geometric Methods for Linear Elliptic and Parabolic Partial Differential Equations written by Shaowu Tang and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Nonlinear Parabolic and Elliptic Equations by : C.V. Pao
Download or read book Nonlinear Parabolic and Elliptic Equations written by C.V. Pao and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 786 pages. Available in PDF, EPUB and Kindle. Book excerpt: In response to the growing use of reaction diffusion problems in many fields, this monograph gives a systematic treatment of a class of nonlinear parabolic and elliptic differential equations and their applications these problems. It is an important reference for mathematicians and engineers, as well as a practical text for graduate students.
Book Synopsis Partial Differential Equations 2 by : Friedrich Sauvigny
Download or read book Partial Differential Equations 2 written by Friedrich Sauvigny and published by Springer Science & Business Media. This book was released on 2006-10-11 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: This encyclopedic work covers the whole area of Partial Differential Equations - of the elliptic, parabolic, and hyperbolic type - in two and several variables. Emphasis is placed on the connection of PDEs and complex variable methods. This second volume addresses Solvability of operator equations in Banach spaces; Linear operators in Hilbert spaces and spectral theory; Schauder's theory of linear elliptic differential equations; Weak solutions of differential equations; Nonlinear partial differential equations and characteristics; Nonlinear elliptic systems with differential-geometric applications. While partial differential equations are solved via integral representations in the preceding volume, this volume uses functional analytic solution methods.
Book Synopsis Nonlinear Methods in Riemannian and Kählerian Geometry by : J. Jost
Download or read book Nonlinear Methods in Riemannian and Kählerian Geometry written by J. Jost and published by Birkhäuser. This book was released on 2013-04-17 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, I present an expanded version of the contents of my lectures at a Seminar of the DMV (Deutsche Mathematiker Vereinigung) in Diisseldorf, June, 1986. The title "Nonlinear methods in complex geometry" already indicates a combination of techniques from nonlinear partial differential equations and geometric concepts. In older geometric investigations, usually the local aspects attracted more attention than the global ones as differential geometry in its foundations provides approximations of local phenomena through infinitesimal or differential constructions. Here, all equations are linear. If one wants to consider global aspects, however, usually the presence of curvature leads to a nonlinearity in the equations. The simplest case is the one of geodesics which are described by a system of second order nonlinear ODE; their linearizations are the Jacobi fields. More recently, nonlinear PDE played a more and more prominent role in geometry. Let us list some of the most important ones: - harmonic maps between Riemannian and Kahlerian manifolds - minimal surfaces in Riemannian manifolds - Monge-Ampere equations on Kahler manifolds - Yang-Mills equations in vector bundles over manifolds. While the solution of these equations usually is nontrivial, it can lead to very signifi cant results in geometry, as solutions provide maps, submanifolds, metrics, or connections which are distinguished by geometric properties in a given context. All these equations are elliptic, but often parabolic equations are used as an auxiliary tool to solve the elliptic ones.
Book Synopsis Equations in Mathematical Physics by : Victor P. Pikulin
Download or read book Equations in Mathematical Physics written by Victor P. Pikulin and published by Springer Science & Business Media. This book was released on 2012-01-05 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many physical processes in fields such as mechanics, thermodynamics, electricity, magnetism or optics are described by means of partial differential equations. The aim of the present book is to demontstrate the basic methods for solving the classical linear problems in mathematical physics of elliptic, parabolic and hyperbolic type. In particular, the methods of conformal mappings, Fourier analysis and Green`s functions are considered, as well as the perturbation method and integral transformation method, among others. Every chapter contains concrete examples with a detailed analysis of their solution.The book is intended as a textbook for students in mathematical physics, but will also serve as a handbook for scientists and engineers.
Book Synopsis Monge Ampere Equation: Applications to Geometry and Optimization by : Luis A. Caffarelli
Download or read book Monge Ampere Equation: Applications to Geometry and Optimization written by Luis A. Caffarelli and published by American Mathematical Soc.. This book was released on 1999 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, the Monge Ampère Equation has received attention for its role in several new areas of applied mathematics: as a new method of discretization for evolution equations of classical mechanics, such as the Euler equation, flow in porous media, Hele-Shaw flow, etc.; as a simple model for optimal transportation and a div-curl decomposition with affine invariance; and as a model for front formation in meteorology and optimal antenna design. These applications were addressed and important theoretical advances presented at a NSF-CBMS conference held at Florida Atlantic University (Boca Raton). L. Cafarelli and other distinguished specialists contributed high-quality research results and up-to-date developments in the field. This is a comprehensive volume outlining current directions in nonlinear analysis and its applications.
Book Synopsis Elliptic and Parabolic Problems by : C Bandle
Download or read book Elliptic and Parabolic Problems written by C Bandle and published by CRC Press. This book was released on 2020-11-26 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Research Note presents some recent advances in various important domains of partial differential equations and applied mathematics including equations and systems of elliptic and parabolic type and various applications in physics, mechanics and engineering. These topics are now part of various areas of science and have experienced tremendous development during the last decades. -------------------------------------
