An integro-differential equation arising as a limit of individual cell-based models |
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| Authors: | M Bodnar JJL Velazquez |
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| Institution: | a Departamento de Matemática Aplicada, Facultad de Ciencias Matemáticas, Universidad Complutense, Avd. Complutense, 28040 Madrid, Spain
b Institute of Applied Mathematics and Mechanics, Faculty of Mathematics, Informatics & Mechanics, Warsaw University, ul. Banacha 2, 02-097 Warszawa, Poland |
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| Abstract: | In this paper, we study mathematical properties of an integro-differential equation that arises as a particular limit case in the study of individual cell-based model. We obtain global well-posedness for some classes of interaction potentials and finite time blow-up for others. The existence of space homogeneous steady states as well as long-time asymptotics for the solutions of the problem is also discussed. |
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