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Long-time behavior of shape design solutions for the Navier-Stokes equations
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SYSNO ASEP 0569947 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Long-time behavior of shape design solutions for the Navier-Stokes equations Author(s) Simon, John Sebastian (MU-W) SAI, ORCID Article number e202100441 Source Title ZAMM-Zeitschrift fur Angewandte Mathematik und Mechanik. - : Wiley - ISSN 0044-2267
Roč. 103, č. 2 (2023)Number of pages 19 s. Language eng - English Country DE - Germany Keywords flow of fluids ; shape optimization Subject RIV BA - General Mathematics OECD category Pure mathematics Method of publishing Limited access Institutional support MU-W - RVO:67985840 UT WOS 000879496700001 EID SCOPUS 85141514214 DOI 10.1002/zamm.202100441 Annotation We investigate the behavior of dynamic shape design problems for fluid flow at large time horizon. In particular, we shall compare the shape solutions of a dynamic shape optimization problem with that of a stationary problem and show that the solution of the former approaches a neighborhood of that of the latter. The convergence of domains is based on the (Formula presented.) -topology of their corresponding characteristic functions, which is closed under the set of domains satisfying the cone property. As a consequence, we show that the asymptotic convergence of shape solutions for parabolic/elliptic problems is a particular case of our analysis. Last, a numerical example is provided to show the occurrence of the convergence of shape design solutions of time-dependent problems with different values of the terminal time T to a shape design solution of the stationary problem. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2024 Electronic address https://doi.org/10.1002/zamm.202100441
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