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Mathematics > Analysis of PDEs

arXiv:1804.03612 (math)
[Submitted on 10 Apr 2018]

Title:Convergence of a Full Discretization for a Second-Order Nonlinear Elastodynamic Equation in Isotropic and Anisotropic Orlicz Spaces

Authors:Adrian Montgomery Ruf
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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.
Comments: 22 pages. The final publication is available at this http URL
Subjects: Analysis of PDEs (math.AP)
MSC classes: 35L20, 47J35, 47H05, 65M12, 65M06, 35M60
Cite as: arXiv:1804.03612 [math.AP]
  (or arXiv:1804.03612v1 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.1804.03612
Journal reference: Zeitschrift für angewandte Mathematik und Physik (2017) 68.5, p. 118,
Related DOI: https://doi.org/10.1007/s00033-017-0863-z

Submission history

From: Adrian Montgomery Ruf [view email]
[v1] Tue, 10 Apr 2018 16:04:01 UTC (94 KB)
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