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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10 citations
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TL;DR: In this paper, the authors apply regularization of divergent integrals in the derivation of the asymptotic expansion of certain multi-dimensional generalized functions, which provides a lucid formulation of the expansion of oscillatory integrals.
10 citations
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TL;DR: In this paper, the occurrence of complicated or erratic asymptotic behavior in non-conservative dynamical systems has been linked by Ruelle and Takens to the appearance of strange attractors.
Abstract: The occurrence of complicated or erratic asymptotic behavior in nonconservative dynamical systems has been linked by Ruelle and Takens to the appearance of strange attractors.' While there are numerical mcthods that indicate the presence of these attractors (e.g.. exponential growth of tangent vectors or continuous frequency spectrums2). there are very few results to date that actually prove the existence of such attractors. Indeed, this has only been done in highly specialized cases (e.g., perturbation of quasi-periodic motion'). One is faced with two fundamental and largely unsolved problems:
10 citations
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TL;DR: In this article, a new notion about the asymptotic stability of Riemann entropy solutions of conservation laws is introduced, and corresponding analytical frameworks are developed, such as zero dissipation limits, uniqueness of entropy solutions, entropy analysis, and divergence-measure fields in L ∞.
Abstract: We are concerned with the asymptotic behavior of entropy solutions of conservation laws. A new notion about the asymptotic stability of Riemann solutions is introduced, and corresponding analytical frameworks are developed. The correlation between the asymptotic problem and many important topics in conservation laws and nonlinear analysis is recognized and analyzed, such as zero dissipation limits, uniqueness of entropy solutions, entropy analysis, and divergence-measure fields in \(L^\infty\). Then this theory is applied to understanding the asymptotic behavior of entropy solutions for many important systems of conservation laws.
10 citations
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10 citations