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Approximation Schemes for Viscosity Solutions of Hamilton-Jacobi Equations

1983 Hamilton-Jacobi equations
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Release : 1983
Genre : Hamilton-Jacobi equations
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Book Synopsis Approximation Schemes for Viscosity Solutions of Hamilton-Jacobi Equations by : Panagiotis E. Souganidis

Download or read book Approximation Schemes for Viscosity Solutions of Hamilton-Jacobi Equations written by Panagiotis E. Souganidis. This book was released on 1983. Available in PDF, EPUB and Kindle. Book excerpt: Equations of Hamilton-Jacobi type arise in many areas of application, including the calculus of variations of variations, control theory and differential games. Recently Crandall and Lions established the correct notion of generalized solutions for these equations. This article discusses the convergence of general approximation schemes to this solution and gives, under certain hypotheses, explicit error estimates. These results are then applied to obtain various representations. These include max-min representations of solutions relevant to the theory of differential games (which imply the existence of the value of the game), representations as limits of solutions of general explicit and implicit finite difference schemes, and as limits of several types of Trotter products. (Author).

Numerical Methods for Viscosity Solutions and Applications

2001 Mathematics
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Release : 2001
Genre : Mathematics
Kind : eBook
Book Rating : 807/5 ( reviews)

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Book Synopsis Numerical Methods for Viscosity Solutions and Applications by : Maurizio Falcone

Download or read book Numerical Methods for Viscosity Solutions and Applications written by Maurizio Falcone. This book was released on 2001. 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.

Semi-Lagrangian Approximation Schemes for Linear and Hamilton-Jacobi Equations

2014-01-31 Mathematics
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Release : 2014-01-31
Genre : Mathematics
Kind : eBook
Book Rating : 04X/5 ( reviews)

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Book Synopsis Semi-Lagrangian Approximation Schemes for Linear and Hamilton-Jacobi Equations by : Maurizio Falcone

Download or read book Semi-Lagrangian Approximation Schemes for Linear and Hamilton-Jacobi Equations written by Maurizio Falcone. This book was released on 2014-01-31. Available in PDF, EPUB and Kindle. Book excerpt: This largely self-contained book provides a unified framework of semi-Lagrangian strategy for the approximation of hyperbolic PDEs, with a special focus on Hamilton-Jacobi equations. The authors provide a rigorous discussion of the theory of viscosity solutions and the concepts underlying the construction and analysis of difference schemes; they then proceed to high-order semi-Lagrangian schemes and their applications to problems in fluid dynamics, front propagation, optimal control, and image processing. The developments covered in the text and the references come from a wide range of literature.

Generalized Solutions of Hamilton-Jacobi Equations

1982 Mathematics
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Release : 1982
Genre : Mathematics
Kind : eBook
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Book Synopsis Generalized Solutions of Hamilton-Jacobi Equations by : Pierre-Louis Lions

Download or read book Generalized Solutions of Hamilton-Jacobi Equations written by Pierre-Louis Lions. This book was released on 1982. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a complete and self-contained treatment of Hamilton-Jacobi equations. The author gives a new presentation of classical methods and of the relations between Hamilton-Jacobi equations and other fields. This complete treatment of both classical and recent aspects of the subject is presented in such a way that it requires only elementary notions of analysis and partial differential equations.

Viscosity Solutions and Applications

2006-11-13 Mathematics
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Release : 2006-11-13
Genre : Mathematics
Kind : eBook
Book Rating : 433/5 ( reviews)

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Book Synopsis Viscosity Solutions and Applications by : Martino Bardi

Download or read book Viscosity Solutions and Applications written by Martino Bardi. This book was released on 2006-11-13. Available in PDF, EPUB and Kindle. Book excerpt: The volume comprises five extended surveys on the recent theory of viscosity solutions of fully nonlinear partial differential equations, and some of its most relevant applications to optimal control theory for deterministic and stochastic systems, front propagation, geometric motions and mathematical finance. The volume forms a state-of-the-art reference on the subject of viscosity solutions, and the authors are among the most prominent specialists. Potential readers are researchers in nonlinear PDE's, systems theory, stochastic processes.

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