Download or read book Vanishing Viscosity Method written by Boling Guo and published by Walter de Gruyter GmbH & Co KG. This book was released on 2016-12-05 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book summarizes several mathematical aspects of the vanishing viscosity method and considers its applications in studying dynamical systems such as dissipative systems, hyperbolic conversion systems and nonlinear dispersion systems. Including original research results, the book demonstrates how to use such methods to solve PDEs and is an essential reference for mathematicians, physicists and engineers working in nonlinear science. Contents: Preface Sobolev Space and Preliminaries The Vanishing Viscosity Method of Some Nonlinear Evolution System The Vanishing Viscosity Method of Quasilinear Hyperbolic System Physical Viscosity and Viscosity of Difference Scheme Convergence of Lax–Friedrichs Scheme, Godunov Scheme and Glimm Scheme Electric–Magnetohydrodynamic Equations References

Download or read book Vanishing Viscosity Method written by and published by . This book was released on 2017 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Vanishing Viscosity Method written by Boling Guo and published by Walter de Gruyter GmbH & Co KG. This book was released on 2016-12-05 with total page 716 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book summarizes several mathematical aspects of the vanishing viscosity method and considers its applications in studying dynamical systems such as dissipative systems, hyperbolic conversion systems and nonlinear dispersion systems. Including original research results, the book demonstrates how to use such methods to solve PDEs and is an essential reference for mathematicians, physicists and engineers working in nonlinear science. Contents: Preface Sobolev Space and Preliminaries The Vanishing Viscosity Method of Some Nonlinear Evolution System The Vanishing Viscosity Method of Quasilinear Hyperbolic System Physical Viscosity and Viscosity of Difference Scheme Convergence of Lax–Friedrichs Scheme, Godunov Scheme and Glimm Scheme Electric–Magnetohydrodynamic Equations References

Download or read book The Vanishing Viscosity Method for Hamilton Jacobi Equations written by Diahong Fu and published by . This book was released on 1992 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Vanishing Viscosity Method in Infinite Dimensions written by Piermarco Cannarsa and published by . This book was released on 1988 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Analysis of the Spectral Vanishing Viscosity Method for Periodic Conservation Laws written by Yvon Maday and published by . This book was released on 1988 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt: We analyze the convergence of the spectral vanishing method for both the spectral and pseudospectral discretizations of the inviscid Burgers' equation. We prove that this kind of vanishing viscosity is responsible for a spectral decay of those Fourier coefficients located toward the end of the computed spectrum; consequently, the discretization error is shown to be spectrally small independent of whether the underlying solution is smooth or not. This in turn implies that the numerical solution remains uniformly bounded and convergence follows by compensated compactness arguments.

Download or read book The Vanishing Viscosity Method in One dimensional Thermoelasticity written by Gui-Qiang Chen and published by . This book was released on 1994 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Spectral Solution of Non linear Conservation Laws Using the Vanishing Viscosity Method written by Raphael Hess and published by . This book was released on 1991 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Recent Developments in Stochastic Methods and Applications written by Albert N. Shiryaev and published by Springer Nature. This book was released on 2021-08-02 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Highlighting the latest advances in stochastic analysis and its applications, this volume collects carefully selected and peer-reviewed papers from the 5th International Conference on Stochastic Methods (ICSM-5), held in Moscow, Russia, November 23-27, 2020. The contributions deal with diverse topics such as stochastic analysis, stochastic methods in computer science, analytical modeling, asymptotic methods and limit theorems, Markov processes, martingales, insurance and financial mathematics, queueing theory and stochastic networks, reliability theory, risk analysis, statistical methods and applications, machine learning and data analysis. The 29 articles in this volume are a representative sample of the 87 high-quality papers accepted and presented during the conference. The aim of the ICSM-5 conference is to promote the collaboration of researchers from Russia and all over the world, and to contribute to the development of the field of stochastic analysis and applications of stochastic models.

Download or read book An Introduction To Viscosity Solutions for Fully Nonlinear PDE with Applications to Calculus of Variations in L written by Nikos Katzourakis and published by Springer. This book was released on 2014-11-26 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to give a quick and elementary, yet rigorous, presentation of the rudiments of the so-called theory of Viscosity Solutions which applies to fully nonlinear 1st and 2nd order Partial Differential Equations (PDE). For such equations, particularly for 2nd order ones, solutions generally are non-smooth and standard approaches in order to define a "weak solution" do not apply: classical, strong almost everywhere, weak, measure-valued and distributional solutions either do not exist or may not even be defined. The main reason for the latter failure is that, the standard idea of using "integration-by-parts" in order to pass derivatives to smooth test functions by duality, is not available for non-divergence structure PDE.

Download or read book Hamilton Jacobi Equations Approximations Numerical Analysis and Applications written by Yves Achdou and published by Springer. This book was released on 2013-05-24 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: These Lecture Notes contain the material relative to the courses given at the CIME summer school held in Cetraro, Italy from August 29 to September 3, 2011. The topic was "Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications". The courses dealt mostly with the following subjects: first order and second order Hamilton-Jacobi-Bellman equations, properties of viscosity solutions, asymptotic behaviors, mean field games, approximation and numerical methods, idempotent analysis. The content of the courses ranged from an introduction to viscosity solutions to quite advanced topics, at the cutting edge of research in the field. We believe that they opened perspectives on new and delicate issues. These lecture notes contain four contributions by Yves Achdou (Finite Difference Methods for Mean Field Games), Guy Barles (An Introduction to the Theory of Viscosity Solutions for First-order Hamilton-Jacobi Equations and Applications), Hitoshi Ishii (A Short Introduction to Viscosity Solutions and the Large Time Behavior of Solutions of Hamilton-Jacobi Equations) and Grigory Litvinov (Idempotent/Tropical Analysis, the Hamilton-Jacobi and Bellman Equations).

Download or read book Numerical Methods for Viscosity Solutions and Applications written by Maurizio Falcone and published by World Scientific. This book was released on 2001 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometrical optics and viscosity solutions / A.-P. Blanc, G. T. Kossioris and G. N. Makrakis -- Computation of vorticity evolution for a cylindrical Type-II superconductor subject to parallel and transverse applied magnetic fields / A. Briggs ... [et al.] -- A characterization of the value function for a class of degenerate control problems / F. Camilli -- Some microstructures in three dimensions / M. Chipot and V. Lecuyer -- Convergence of numerical schemes for the approximation of level set solutions to mean curvature flow / K. Deckelnick and G. Dziuk -- Optimal discretization steps in semi-lagrangian approximation of first-order PDEs / M. Falcone, R. Ferretti and T. Manfroni -- Convergence past singularities to the forced mean curvature flow for a modified reaction-diffusion approach / F. Fierro -- The viscosity-duality solutions approach to geometric pptics for the Helmholtz equation / L. Gosse and F. James -- Adaptive grid generation for evolutive Hamilton-Jacobi-Bellman equations / L. Grune -- Solution and application of anisotropic curvature driven evolution of curves (and surfaces) / K. Mikula -- An adaptive scheme on unstructured grids for the shape-from-shading problem / M. Sagona and A. Seghini -- On a posteriori error estimation for constant obstacle problems / A. Veeser.

Download or read book Hamilton Jacobi Equations written by Hung V. Tran and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an extensive survey of many important topics in the theory of Hamilton–Jacobi equations with particular emphasis on modern approaches and viewpoints. Firstly, the basic well-posedness theory of viscosity solutions for first-order Hamilton–Jacobi equations is covered. Then, the homogenization theory, a very active research topic since the late 1980s but not covered in any standard textbook, is discussed in depth. Afterwards, dynamical properties of solutions, the Aubry–Mather theory, and weak Kolmogorov–Arnold–Moser (KAM) theory are studied. Both dynamical and PDE approaches are introduced to investigate these theories. Connections between homogenization, dynamical aspects, and the optimal rate of convergence in homogenization theory are given as well. The book is self-contained and is useful for a course or for references. It can also serve as a gentle introductory reference to the homogenization theory.

Download or read book Optimal Control and Viscosity Solutions of Hamilton Jacobi Bellman Equations written by Martino Bardi and published by Springer Science & Business Media. This book was released on 2009-05-21 with total page 588 pages. Available in PDF, EPUB and Kindle. Book excerpt: This softcover book is a self-contained account of the theory of viscosity solutions for first-order partial differential equations of Hamilton–Jacobi type and its interplay with Bellman’s dynamic programming approach to optimal control and differential games. It will be of interest to scientists involved in the theory of optimal control of deterministic linear and nonlinear systems. The work may be used by graduate students and researchers in control theory both as an introductory textbook and as an up-to-date reference book.

Download or read book A Spectral Vanishing Viscosity Method for Stabilizing Low Dimensional Galerkin Systems written by and published by . This book was released on 2002 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: Low-dimensional flow dynamical systems are susceptible to instabilities after long-time integration. In this paper, we investigate the stability of such two-dimensional models constructed from Karhunen-Loeve expansions for flows past a circular cylinder. We first demonstrate that although the short-term dynamics may be predicted accurately with only a handful of modes retained, instabilities arise after a few hundred vortex shedding cycles. We then propose a dissipative model based on a spectral vanishing viscosity (SVV) diffusion convolution operator as an effective way of stabilizing low-dimensional Galerkin systems.

Download or read book Numerical Methods for Conservation Laws written by LEVEQUE and published by Birkhäuser. This book was released on 2013-11-11 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes developed from a course on the numerical solution of conservation laws first taught at the University of Washington in the fall of 1988 and then at ETH during the following spring. The overall emphasis is on studying the mathematical tools that are essential in de veloping, analyzing, and successfully using numerical methods for nonlinear systems of conservation laws, particularly for problems involving shock waves. A reasonable un derstanding of the mathematical structure of these equations and their solutions is first required, and Part I of these notes deals with this theory. Part II deals more directly with numerical methods, again with the emphasis on general tools that are of broad use. I have stressed the underlying ideas used in various classes of methods rather than present ing the most sophisticated methods in great detail. My aim was to provide a sufficient background that students could then approach the current research literature with the necessary tools and understanding. vVithout the wonders of TeX and LaTeX, these notes would never have been put together. The professional-looking results perhaps obscure the fact that these are indeed lecture notes. Some sections have been reworked several times by now, but others are still preliminary. I can only hope that the errors are not too blatant. Moreover, the breadth and depth of coverage was limited by the length of these courses, and some parts are rather sketchy.

Download or read book Asymptotic Series and the Method of Vanishing Viscosity written by University of Minnesota. Institute for Mathematics and Its Applications and published by . This book was released on 1985 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: