Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5772420 | Journal of Functional Analysis | 2017 | 52 Pages |
Abstract
We consider the semilinear wave equation with focusing energy-critical nonlinearity in space dimension N=5âttu=Îu+|u|4/3u, with radial data. It is known [7] that a solution (u,âtu) which blows up at t=0 in a neighborhood (in the energy norm) of the family of solitons Wλ, decomposes in the energy space as(u(t),âtu(t))=(Wλ(t)+u0â,u1â)+o(1), where limtâ0â¡Î»(t)/t=0 and (u0â,u1â)âHË1ÃL2. We construct a blow-up solution of this type such that the asymptotic profile (u0â,u1â) is any pair of sufficiently regular functions with u0â(0)>0. For these solutions the concentration rate is λ(t)â¼t4. We also provide examples of solutions with concentration rate λ(t)â¼tν+1 for ν>8, related to the behavior of the asymptotic profile near the origin.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Jacek Jendrej,