Aggregation Equation and Collapse to Singular Measure
Tutorials, Schools, and Workshops in the Mathematical Sciences, ISSN: 2522-0977, Page: 123-149
2022
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Example: if you select the 1-year option for an article published in 2019 and a metric category shows 90%, that means that the article or review is performing better than 90% of the other articles/reviews published in that journal in 2019. If you select the 3-year option for the same article published in 2019 and the metric category shows 90%, that means that the article or review is performing better than 90% of the other articles/reviews published in that journal in 2019, 2018 and 2017.
Citation Benchmarking is provided by Scopus and SciVal and is different from the metrics context provided by PlumX Metrics.
Book Chapter Description
We are concerned with the dynamics of onefold symmetric patches for the two-dimensional aggregation equation associated with the Newtonian potential. We reformulate a suitable graph model and prove a local well-posedness result in subcritical and critical spaces. The global existence is obtained only for small initial data using a weak damping property hidden in the velocity terms. This allows to analyze the concentration phenomenon of the aggregation patches near the blowup time. In particular, we prove that the patch collapses to a collection of disjoint segments, and we provide a description of the singular measure through a careful study of the asymptotic behavior of the graph.
Bibliographic Details
http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=85142095956&origin=inward; http://dx.doi.org/10.1007/978-3-031-14268-0_4; https://link.springer.com/10.1007/978-3-031-14268-0_4; https://dx.doi.org/10.1007/978-3-031-14268-0_4; https://link.springer.com/chapter/10.1007/978-3-031-14268-0_4
Springer Science and Business Media LLC
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