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1 results

Convergence of a Time Discretization for a Nonlinear Second-Order Inclusion
Part of
- Existence theories
- Equations and inequalities involving nonlinear operators
Krzysztof Bartosz, Leszek Gasiński, Zhenhai Liu, Paweł Szafraniec
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 61 / Issue 1 / February 2018

Published online by Cambridge University Press:

29 May 2017, pp. 93-120
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We study an abstract second order inclusion involving two nonlinear single-valued operators and a nonlinear multi-valued term. Our goal is to establish the existence of solutions to the problem by applying numerical scheme based on time discretization. We show that the sequence of approximate solution converges weakly to a solution of the exact problem. We apply our abstract result to a dynamic, second-order-in-time differential inclusion involving a Clarke subdifferential of a locally Lipschitz, possibly non-convex and non-smooth potential. In the two presented examples the Clarke subdifferential appears either in a source term or in a boundary term.