Regularity and multi-scale discretization of the solution construction of hyperbolic evolution equations with limited smoothness
نویسندگان
چکیده
Article history: Received 4 July 2011 Revised 20 December 2011 Accepted 30 January 2012 Available online 1 February 2012 Communicated by Gregory Beylkin
منابع مشابه
Regularity In, and Multi-scale Discretization of the Solution Construction of Hyperbolic Evolution Equations of Limited Smoothness
We present a multi-scale solution scheme for hyperbolic evolution equations with curvelets. We assume, essentially, that the second-order derivatives of the symbol of the evolution operator are uniformly Lipschitz. The scheme is based on a solution construction introduced by Smith [19] and is composed of generating an approximate solution following a paradifferential decomposition of the mentio...
متن کاملA multi-scale approach to hyperbolic evolution equations
We discuss how techniques frommultiresolution analysis and phase space transforms can be exploited in solving a general class of evolution equations with limited smoothness. We have wave propagation in media of limited smoothness in mind. The frame that appears naturally in this context is closely related to the one formed by curvelets. The construction considered here implies a full-wave descr...
متن کاملA Multi-Scale Approach to Hyperbolic Evolution Equations with Limited Smoothness
A Multi-Scale Approach to Hyperbolic Evolution Equations with Limited Smoothness Fredrik Andersson a , Maarten V. de Hoop b , Hart F. Smith c & Gunther Uhlmann c a Centre for Mathematical Sciences , Lund Institute of Technology/ Lund University , Lund, Sweden b Center for Computational and Applied Mathematics , Purdue University , West Lafayette, Indiana, USA c Department of Mathematics , Unive...
متن کاملThe new implicit finite difference scheme for two-sided space-time fractional partial differential equation
Fractional order partial differential equations are generalizations of classical partial differential equations. Increasingly, these models are used in applications such as fluid flow, finance and others. In this paper we examine some practical numerical methods to solve a class of initial- boundary value fractional partial differential equations with variable coefficients on a finite domain. S...
متن کاملBackward Euler discretization of fully nonlinear parabolic problems
This paper is concerned with the time discretization of nonlinear evolution equations. We work in an abstract Banach space setting of analytic semigroups that covers fully nonlinear parabolic initial-boundary value problems with smooth coefficients. We prove convergence of variable stepsize backward Euler discretizations under various smoothness assumptions on the exact solution. We further sho...
متن کامل