Journal article
ON A NONLOCAL AGGREGATION MODEL WITH NONLINEAR DIFFUSION
Discrete and continuous dynamical systems, Vol.27(1), pp.301-323
05/01/2010
DOI: 10.3934/dcds.2010.27.301
Abstract
We consider a nonlocal aggregation equation with nonlinear diffusion which arises from the study of biological aggregation dynamics. As a degenerate parabolic problem, we prove the well-posedness, continuation criteria and smoothness of local solutions. For compactly supported nonnegative smooth initial data we prove that the gradient of the solution develops L(x)(infinity) norm blowup in finite time.
Details
- Title: Subtitle
- ON A NONLOCAL AGGREGATION MODEL WITH NONLINEAR DIFFUSION
- Creators
- Dong Li - Univ Iowa, Dept Math, Iowa City, IA 52242 USAXiaoyi Zhang - Univ Iowa, Dept Math, Iowa City, IA 52242 USA
- Resource Type
- Journal article
- Publication Details
- Discrete and continuous dynamical systems, Vol.27(1), pp.301-323
- DOI
- 10.3934/dcds.2010.27.301
- ISSN
- 1078-0947
- eISSN
- 1553-5231
- Publisher
- AMER INST MATHEMATICAL SCIENCES
- Number of pages
- 23
- Grant note
- Mathematics Department of University of Iowa Project 973 University of Iowa Knowledge Innovation Program of CAS DMS-0635607; 10601060; 0908032 / NSF
- Language
- English
- Date published
- 05/01/2010
- Academic Unit
- Mathematics
- Record Identifier
- 9984240762202771
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