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Lectures on Nonlinear Hyperbolic Differential Equations

1997-07-17 Mathematics
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Release : 1997-07-17
Genre : Mathematics
Kind : eBook
Book Rating : 214/5 ( reviews)

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Book Synopsis Lectures on Nonlinear Hyperbolic Differential Equations by : Lars Hörmander

Download or read book Lectures on Nonlinear Hyperbolic Differential Equations written by Lars Hörmander. This book was released on 1997-07-17. Available in PDF, EPUB and Kindle. Book excerpt: In this introductory textbook, a revised and extended version of well-known lectures by L. Hörmander from 1986, four chapters are devoted to weak solutions of systems of conservation laws. Apart from that the book only studies classical solutions. Two chapters concern the existence of global solutions or estimates of the lifespan for solutions of nonlinear perturbations of the wave or Klein-Gordon equation with small initial data. Four chapters are devoted to microanalysis of the singularities of the solutions. This part assumes some familiarity with pseudodifferential operators which are standard in the theory of linear differential operators, but the extension to the more exotic classes of opertors needed in the nonlinear theory is presented in complete detail.

Advanced Numerical Approximation of Nonlinear Hyperbolic Equations

2006-11-14 Mathematics
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Release : 2006-11-14
Genre : Mathematics
Kind : eBook
Book Rating : 044/5 ( reviews)

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Book Synopsis Advanced Numerical Approximation of Nonlinear Hyperbolic Equations by : B. Cockburn

Download or read book Advanced Numerical Approximation of Nonlinear Hyperbolic Equations written by B. Cockburn. This book was released on 2006-11-14. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the texts of the four series of lectures presented by B.Cockburn, C.Johnson, C.W. Shu and E.Tadmor at a C.I.M.E. Summer School. It is aimed at providing a comprehensive and up-to-date presentation of numerical methods which are nowadays used to solve nonlinear partial differential equations of hyperbolic type, developing shock discontinuities. The most effective methodologies in the framework of finite elements, finite differences, finite volumes spectral methods and kinetic methods, are addressed, in particular high-order shock capturing techniques, discontinuous Galerkin methods, adaptive techniques based upon a-posteriori error analysis.

Lectures on Non-linear Wave Equations

2008 Mathematics
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Release : 2008
Genre : Mathematics
Kind : eBook
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Book Synopsis Lectures on Non-linear Wave Equations by : Christopher Donald Sogge

Download or read book Lectures on Non-linear Wave Equations written by Christopher Donald Sogge. This book was released on 2008. Available in PDF, EPUB and Kindle. Book excerpt: Presents an account of the basic facts concerning the linear wave equation and the methods from harmonic analysis that are necessary when studying nonlinear hyperbolic differential equations. This book examines quasilinear equations with small data where the Klainerman-Sobolev inequalities and weighted space-time estimates are introduced.

Lecture Notes on Numerical Methods for Hyperbolic Equations

2011-05-23 Mathematics
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Release : 2011-05-23
Genre : Mathematics
Kind : eBook
Book Rating : 627/5 ( reviews)

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Book Synopsis Lecture Notes on Numerical Methods for Hyperbolic Equations by : Elena Vázquez-Cendón

Download or read book Lecture Notes on Numerical Methods for Hyperbolic Equations written by Elena Vázquez-Cendón. This book was released on 2011-05-23. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the lecture notes of the Short Course on Numerical Methods for Hyperbolic Equations (Faculty of Mathematics, University of Santiago de Compostela, Spain, 2-4 July 2011). The course was organized in recognition of Prof. Eleuterio Toro‘s contribution to education and training on numerical methods for partial differential equation

Propagation and Interaction of Singularities in Nonlinear Hyperbolic Problems

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
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Book Rating : 540/5 ( reviews)

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Book Synopsis Propagation and Interaction of Singularities in Nonlinear Hyperbolic Problems by : Michael Beals

Download or read book Propagation and Interaction of Singularities in Nonlinear Hyperbolic Problems written by Michael Beals. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: This book developed from a series of lectures I gave at the Symposium on Nonlinear Microlocal Analysis held at Nanjing University in October. 1988. Its purpose is to give an overview of the use of microlocal analysis and commutators in the study of solutions to nonlinear wave equations. The weak singularities in the solutions to such equations behave up to a certain extent like those present in the linear case: they propagate along the null bicharacteristics of the operator. On the other hand. examples exhibiting singularities not present in the linear case can also be constructed. I have tried to present a crossection of both the regularity results and the singular examples. for problems on the interior of a domain and on domains with boundary. The main emphasis is on the case of more than one space dimen sion. since that case is treated in great detail in the paper of Rauch-Reed 159]. The results presented here have for the most part appeared elsewhere. and are the work of many authors. but a few new examples and proofs are given. I have attempted to indicate the essential ideas behind the arguments. so that only some of the results are proved in full detail. It is hoped that the central notions of the more technical proofs appearing in research papers will be illuminated by these simpler cases.

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