Journal article
Exploding solutions for a nonlocal quadratic evolution problem
Revista matemática iberoamericana, Vol.26(1), pp.295-332
01/01/2010
DOI: 10.4171/RMI/602
Abstract
We consider a nonlinear parabolic equation with fractional diffusion which arises from modelling chemotaxis in bacteria. We prove the wellposedness, continuation criteria, and smoothness of local solutions. In the repulsive case we prove global wellposedness in Sobolev spaces. Finally in the attractive case, we prove that for a class of smooth initial data the L(x)(infinity)-norm of the corresponding solution blows up in finite time. This solves a problem left open by Biler and Woyczynski [8].
Details
- Title: Subtitle
- Exploding solutions for a nonlocal quadratic evolution problem
- Creators
- Dong Li - Univ Iowa, Dept Math, Iowa City, IA 52240 USAJose L Rodrigo - Coventry (United Kingdom)Xiaoyi Zhang - Univ Iowa, Dept Math, Iowa City, IA 52240 USA
- Resource Type
- Journal article
- Publication Details
- Revista matemática iberoamericana, Vol.26(1), pp.295-332
- DOI
- 10.4171/RMI/602
- ISSN
- 0213-2230
- eISSN
- 2235-0616
- Publisher
- UNIV AUTONOMA MADRID
- Number of pages
- 38
- Grant note
- DMS-0635607; DMS-0908032; 10601060 / National Science Foundation Math. Department of University of Iowa project 973 in China MTM2005-05980 / Ministerio de Educacion y Ciencia (Spain)
- Language
- English
- Date published
- 01/01/2010
- Academic Unit
- Mathematics
- Record Identifier
- 9984241058802771
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