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Convergence of a full discretization for a second-order nonlinear elastodynamic equation in isotropic and anisotropic Orlicz spaces

  • A. M. Ruf
Article

Abstract

In this paper, we study a second-order, nonlinear evolution equation with damping arising in elastodynamics. The nonlinear term is monotone and possesses a convex potential but exhibits anisotropic and nonpolynomial growth. The appropriate setting for such equations is that of monotone operators in Orlicz spaces. Global existence of solutions in the sense of distributions is shown via convergence of the backward Euler scheme combined with an internal approximation. Moreover, we show uniqueness in a class of sufficiently smooth solutions and provide an a priori error estimate for the temporal semidiscretization.

Keywords

Nonlinear evolution equation of second order in time with damping Elastodynamics Monotone operator Nonpolynomial growth Anisotropic Orlicz space Existence Full discretization Convergence 

Mathematics Subject Classification

35L20 47J35 47H05 65M12 65M06 35M60 

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of OsloOsloNorway

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