Some Problems on Nonlinear Hyperbolic Equations and Applications

Some Problems on Nonlinear Hyperbolic Equations and Applications
Author: Yuejun Peng
Publisher: World Scientific
Total Pages: 464
Release: 2010
Genre: Mathematics
ISBN: 9814322881

This volume is composed of two parts: Mathematical and Numerical Analysis for Strongly Nonlinear Plasma Models and Exact Controllability and Observability for Quasilinear Hyperbolic Systems and Applications. It presents recent progress and results obtained in the domains related to both subjects without attaching much importance to the details of proofs but rather to difficulties encountered, to open problems and possible ways to be exploited. It will be very useful for promoting further study on some important problems in the future.

Lectures on Nonlinear Hyperbolic Differential Equations

Lectures on Nonlinear Hyperbolic Differential Equations
Author: Lars Hörmander
Publisher: Springer Science & Business Media
Total Pages: 308
Release: 1997-07-17
Genre: Mathematics
ISBN: 9783540629214

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.

Abstract and Applied Analysis

Abstract and Applied Analysis
Author: N. M. Chuong
Publisher: World Scientific
Total Pages: 579
Release: 2004
Genre: History
ISBN: 981238944X

This volume takes up various topics in Mathematical Analysis including boundary and initial value problems for Partial Differential Equations and Functional Analytic methods.Topics include linear elliptic systems for composite material ? the coefficients may jump from domain to domain; Stochastic Analysis ? many applied problems involve evolution equations with random terms, leading to the use of stochastic analysis.The proceedings have been selected for coverage in: ? Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)? CC Proceedings ? Engineering & Physical Sciences

Theory, Numerics and Applications of Hyperbolic Problems II

Theory, Numerics and Applications of Hyperbolic Problems II
Author: Christian Klingenberg
Publisher: Springer
Total Pages: 698
Release: 2018-06-27
Genre: Mathematics
ISBN: 3319915487

The second of two volumes, this edited proceedings book features research presented at the XVI International Conference on Hyperbolic Problems held in Aachen, Germany in summer 2016. It focuses on the theoretical, applied, and computational aspects of hyperbolic partial differential equations (systems of hyperbolic conservation laws, wave equations, etc.) and of related mathematical models (PDEs of mixed type, kinetic equations, nonlocal or/and discrete models) found in the field of applied sciences.

Finite Volume Methods for Hyperbolic Problems

Finite Volume Methods for Hyperbolic Problems
Author: Randall J. LeVeque
Publisher: Cambridge University Press
Total Pages: 582
Release: 2002-08-26
Genre: Mathematics
ISBN: 1139434187

This book, first published in 2002, contains an introduction to hyperbolic partial differential equations and a powerful class of numerical methods for approximating their solution, including both linear problems and nonlinear conservation laws. These equations describe a wide range of wave propagation and transport phenomena arising in nearly every scientific and engineering discipline. Several applications are described in a self-contained manner, along with much of the mathematical theory of hyperbolic problems. High-resolution versions of Godunov's method are developed, in which Riemann problems are solved to determine the local wave structure and limiters are then applied to eliminate numerical oscillations. These methods were originally designed to capture shock waves accurately, but are also useful tools for studying linear wave-propagation problems, particularly in heterogenous material. The methods studied are implemented in the CLAWPACK software package and source code for all the examples presented can be found on the web, along with animations of many of the simulations. This provides an excellent learning environment for understanding wave propagation phenomena and finite volume methods.

Multi-dimensional Hyperbolic Partial Differential Equations

Multi-dimensional Hyperbolic Partial Differential Equations
Author: Sylvie Benzoni-Gavage
Publisher: Oxford University Press, USA
Total Pages: 535
Release: 2007
Genre: Mathematics
ISBN: 019921123X

Authored by leading scholars, this comprehensive text presents a view of the multi-dimensional hyperbolic partial differential equations, with a particular emphasis on problems in which modern tools of analysis have proved useful. It is useful to graduates and researchers in both hyperbolic PDEs and compressible fluid dynamics.

Nonlinear Hyperbolic Equations — Theory, Computation Methods, and Applications

Nonlinear Hyperbolic Equations — Theory, Computation Methods, and Applications
Author: Josef Ballmann
Publisher: Springer Science & Business Media
Total Pages: 729
Release: 2013-03-08
Genre: Technology & Engineering
ISBN: 3322878694

On the occasion of the International Conference on Nonlinear Hyperbolic Problems held in St. Etienne, France, 1986 it was decided to start a two years cycle of conferences on this very rapidly expanding branch of mathematics and it·s applications in Continuum Mechanics and Aerodynamics. The second conference toolc place in Aachen, FRG, March 14-18, 1988. The number of more than 200 participants from more than 20 countries all over the world and about 100 invited and contributed papers, well balanced between theory, numerical analysis and applications, do not leave any doubt that it was the right decision to start this cycle of conferences, of which the third will be organized in Sweden in 1990. ThiS volume contains sixty eight original papers presented at the conference, twenty two cif them dealing with the mathematical theory, e.g. existence, uniqueness, stability, behaviour of solutions, physical modelling by evolution equations. Twenty two articles in numerical analysis are concerned with stability and convergence to the physically relevant solutions such as schemes especially deviced for treating shoclcs, contact discontinuities and artificial boundaries. Twenty four papers contain multidimensional computational applications to nonlinear waves in solids, flow through porous media and compressible fluid flow including shoclcs, real gas effects, multiphase phenomena, chemical reactions etc. The editors and organizers of the Second International Conference on Hyperbolic Problems would lilce to thanlc the Scientific Committee for the generous support of recommending invited lectures and selecting the contributed papers of the conference.

Control Of Partial Differential Equations

Control Of Partial Differential Equations
Author: Jean-michel Coron
Publisher: World Scientific
Total Pages: 315
Release: 2023-04-11
Genre: Mathematics
ISBN: 981127164X

This book is mainly a collection of lecture notes for the 2021 LIASFMA International Graduate School on Applied Mathematics. It provides the readers some important results on the theory, the methods, and the application in the field of 'Control of Partial Differential Equations'. It is useful for researchers and graduate students in mathematics or control theory, and for mathematicians or engineers with an interest in control systems governed by partial differential equations.

Nonlinear Hyperbolic Equations and Field Theory

Nonlinear Hyperbolic Equations and Field Theory
Author: M K V Murthy
Publisher: CRC Press
Total Pages: 242
Release: 1992-03-30
Genre: Mathematics
ISBN: 9780582087668

Contains the proceedings of a workshop on nonlinear hyperbolic equations held at Varenna, Italy in June 1990.

New Tools for Nonlinear PDEs and Application

New Tools for Nonlinear PDEs and Application
Author: Marcello D'Abbicco
Publisher: Springer
Total Pages: 392
Release: 2019-05-07
Genre: Mathematics
ISBN: 3030109372

This book features a collection of papers devoted to recent results in nonlinear partial differential equations and applications. It presents an excellent source of information on the state-of-the-art, new methods, and trends in this topic and related areas. Most of the contributors presented their work during the sessions "Recent progress in evolution equations" and "Nonlinear PDEs" at the 12th ISAAC congress held in 2017 in Växjö, Sweden. Even if inspired by this event, this book is not merely a collection of proceedings, but a stand-alone project gathering original contributions from active researchers on the latest trends in nonlinear evolution PDEs.