Emmrich, EtienneWeckner, Olaf2019-01-082019-01-0820071081-2865https://depositonce.tu-berlin.de/handle/11303/8848http://dx.doi.org/10.14279/depositonce-7977Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.Long-range interactions for linearly elastic media resulting in nonlinear dispersion relations are modeled 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 ∞(ℝ) as well as jump relations are proved. Moreover, the construction of the micromodulus function from the dispersion relation is studied. 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.en510 Mathematik620 Ingenieurwissenschaften und zugeordnete Tätigkeitenlong-range interactionsperidynamic theorynonlinear dispersion relationsintegro-differential equationexistence and uniquenessjump discontinuitynumerical approximationArticle1741-3028