2024-03-29T12:18:09Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/697752022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116Asymptotic behavior of type I blowup solutions to a parabolic-elliptic system of drift-diffusion typeYoshikazu, GigaNoriko, MizoguchiTakasi, Senba410A Cauchy problem for a parabolic-elliptic system of drift-di usion type is considered. The problem is formally of the form Ut = r (rU Ur( )1U): This system describes a mass-conserving aggregation phenomenon including gravitational collapse and bacterial chemotaxis. Our concern is the asymptotic behavior of blowup solutions when the blowup is type I in the sense that its blowup rate is the same as the corresponding ordinary di erential equation yt = y2 (up to a multiple constant). It is shown that all type I blowup is asymptotically (backward) self-similar provided that the solution is radial, nonnegative when the blowup set is a singleton and the space dimension is greater than or equal to three. 2000 Mathematics Subject Classi cation. 35K55, 35K57, 92C17. 1Department of Mathematics, Hokkaido UniversityDepartmental Bulletin Paperapplication/pdfhttp://hdl.handle.net/2115/69775info:doi/10.14943/84115https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69775/1/pre968.pdfHokkaido University Preprint Series in Mathematics9681302010-09-03engpublisher