2019-10-23T10:08:42Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/693432018-04-25T23:44:07Zhdl_2115_45007hdl_2115_116On blow up rate for sign-changing solutions in a convex domainGiga, Y.Matsui, S.Sasayama, S.410This paper studies a growth rate of a solution blowing up at time T of the semilinear heat equation Ut - £:iu - lulP-1u = 0 in a convex domain D in Rn with zero-boundary condition. For a subcritical p E (1, (n + 2)/(n - 2)) a growth rate estimate lu(x, t)I :S C(T- t)-1/(p-l), x E D, t E (0, T) is established with C independent oft provided that D is uniformly 02. The estimate applies to sign-changing solutions. The same estimate has been recently established when D = Rn by authors. The proof is similar but we need to establish Lh - Lk estimate for a time-dependent domain because of the presence of the boundary.Departmental Bulletin Paperapplication/pdfhttp://hdl.handle.net/2115/69343info:doi/10.14943/83739https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69343/1/pre594.pdfHokkaido University Preprint Series in Mathematics5941122003-07engpublisher