ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Non-Autonomous Dynamics and Product Formula Approximation of Solution Operator

Discontinuity, Nonlinearity, and Complexity 9(4) (2020) 579--590 | DOI:10.5890/DNC.2020.12.011

Valentin A. Zagrebnov

Institut de Math'{e}matiques de Marseille - AMU, CMI - Technop^{o}le Ch^{a}teau-Gombert, 39 rue F. Joliot Curie, 13453 Marseille, France

Abstract

The paper is devoted to non-autonomous dynamics, which is generated by positive self-adjoint operator $A$ and a family of non-negative self-adjoint operators $\{B(t)\}_{t\geq 0}$ defined in a separable Hilbert space. It is shown that solution operator $\{U(t,s)\}_{0 \leq s \leq t}$ of the evolution equation can be approximated in the operator norm topology by a product formula that involves $A$ and $B(t)$. We also established the rate of convergence of the product formula to the solution operator. These results are proved using the evolution semigroup approach to non-autonomous dynamics.

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