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Main Title: Analysis and numerical approximation of an integro-differential equation modelling non-local effects in linear elasticity
Author(s): Emmrich, Etienne
Weckner, Olaf
Type: Research Paper
Abstract: Long-range interactions for linearly elastic media resulting in nonlinear dispersion relations are modelled by an initial-value problem for an integro-differential equation (IDE) that incorporates non-local effects. Interpreting this IDE as an evolutionary equation of second order, well-posedness in $L^{\infty}(\rz)$ as well as jump relations are proved. A numerical approximation based upon quadrature is suggested and carried out for two examples, one involving jump discontinuities in the initial data corresponding to a Riemann-like problem.
Subject(s): long-range interactions
peridynamic theory
nonlinear dispersion relations
integro-differential equation
existence and uniqueness
jump discontinuity
numerical approximation
Issue Date: 2-Feb-2005
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 74H20 Existence of solutions
74H25 Uniqueness of solutions
74H30 Regularity of solutions
74H55 Stability
74H15 Numerical approximation of solutions
74B99 None of the above, but in this section
45K05 Integro-partial differential equations
34G10 Linear equations
47G20 Integro-differential operators
65R20 Integral equations
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2005, 02
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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