Projects per year
We consider the problem vt=Δv+|v|p−1vin Ω×(0,T),v=0on ∂Ω×(0,T),v>0in Ω×(0,T). In a domain Ω⊂Rd, d≥7 enjoying special symmetries, we find the first example of a solution with type II blow-up for a power p less than the Joseph-Lundgren exponent [Formula presented] No type II radial blow-up is present for p<pJL(d). We take [Formula presented], the Sobolev critical exponent in one dimension less. The solution blows up on circle contained in a negatively curved part of the boundary in the form of a sharply scaled Aubin-Talenti bubble, approaching its energy density a Dirac measure for the curve. This is a completely new phenomenon for a diffusion setting.
|Journal||Journal of Functional Analysis|
|Early online date||28 Sept 2020|
|Publication status||Published - 1 Jan 2021|
- Parabolic equation
- Type II blow up phenomena
ASJC Scopus subject areas
FingerprintDive into the research topics of 'Geometry driven type II higher dimensional blow-up for the critical heat equation'. Together they form a unique fingerprint.
- 1 Active
Concentration phenomena in nonlinear analysis
Engineering and Physical Sciences Research Council
27/04/20 → 31/03/24
Project: Research council