Local and nonlocal diffusion in mathematical biology
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Organizer(s): |
Name:
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Affiliation:
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Country:
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Jakub Skrzeczkowski
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Mathematical Institute, University of Oxford
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England
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Jose Antonio Carrillo
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Mathematical Institute, University of Oxford
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England
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Yihong Du
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University of New England
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Australia
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Introduction:
| | In recent years, there has been significant interest and progress in the mathematical analysis of diffusion-type partial differential equations, which are ubiquitous in mathematical biology and used to model phenomena at various scales, from cell-cell adhesion to population dynamics. This session will provide an opportunity to present recent advances and discuss new challenges in this field. We focus our attention on both local and nonlocal PDEs, including the mathematical theory of reaction-diffusion, porous media, aggregation-diffusion, Keller-Segel, and Cahn-Hilliard equations. Some of the topics we aim to cover include classical well-posedness theory and qualitative properties of solutions (such as asymptotic behavior, traveling waves, and pattern formation), as well as singular limits, with a particular emphasis on connections between nonlocal equations and their local counterparts. By bringing together researchers at various stages of their careers, we hope to create a platform for exchanging ideas and fostering new collaborations. |
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