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Equations of second order in time with quasilinear damping: existence in Orlicz spaces via convergence of a full discretisation
Author(s) -
Emmrich Etienne,
Šiška David,
WróblewskaKamińska Aneta
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3706
Subject(s) - mathematics , monotone polygon , discretization , convergence (economics) , mathematical analysis , nonlinear system , order (exchange) , backward euler method , geometry , physics , finance , quantum mechanics , economics , economic growth
A nonlinear evolution equation of second order with damping is studied. The quasilinear damping term is monotone and coercive 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. Copyright © 2015 John Wiley & Sons, Ltd.