Li, Dong, Rodrigo, Jose L. and Zhang, Xiaoyi (2010) Exploding solutions for a nonlocal quadratic evolution problem. Revista Matematica Iberoamericana, Vol.26 (No.1). pp. 295-332. ISSN 0213-2230.

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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].

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Journal or Publication Title:	Revista Matematica Iberoamericana
Publisher:	European Mathematical Society Publishing House
ISSN:	0213-2230
Official Date:	2010
Dates:	Date Event 2010 Published
Volume:	Vol.26
Number:	No.1
Number of Pages:	38
Page Range:	pp. 295-332
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Funder:	National Science Foundation, Math. Department of University of Iowa, project 973 in China, Ministerio de Educacion y Ciencia (Spain)
Grant number:	DMS-0635607, DMS-0908032, 10601060, MTM2005-05980

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