Topic
Asymptotology
About: Asymptotology is a research topic. Over the lifetime, 1319 publications have been published within this topic receiving 35831 citations.
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01 Jan 1980
83 citations
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TL;DR: In this article, the case of the steady-state Navier-Stokes equations for an incompressible fluid and a no-slip condition prescribed on the boundary of an arbitrary shaped obstacle is addressed.
Abstract: The aim of the topological asymptotic analysis is to provide an asymptotic expansion of a shape functional with respect to the size of a small inclusion inserted inside the domain. The main field of application is shape optimization. This paper addresses the case of the steady-state Navier-Stokes equations for an incompressible fluid and a no-slip condition prescribed on the boundary of an arbitrary shaped obstacle. The two and three dimensional cases are treated for several examples of cost functional and a numerical application is presented.
78 citations
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78 citations
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TL;DR: In this paper, the authors show how to obtain the full asymptotic expansion for solutions of integrable wave equations to all orders, as t→∞, without relying on an a priori ansatz for the form of the solution.
Abstract: The authors show how to obtain the full asymptotic expansion for solutions of integrable wave equations to all orders, as t→∞. The method is rigorous and systematic and does not rely on an a priori ansatz for the form of the solution.
76 citations