Blow-up rates for a fractional heat equation
Articles
Overview
published in
publication date
- May 2021
start page
- 2011
end page
- 2018
issue
- 5
volume
- 149
Digital Object Identifier (DOI)
full text
International Standard Serial Number (ISSN)
- 0002-9939
Electronic International Standard Serial Number (EISSN)
- 1088-6826
abstract
-
We study the speed at which nonglobal solutions to the fractional
heat equation
ut + (−Δ)α/2u = up,
with 0 1, tend to infinity. We prove that, assuming either
p < pF ≡ 1 + α/N or u is strictly increasing in time, then for t close to
the blow-up time T it holds that u(ยท, t) ∞ ∼ (T − t)
− 1/p−1 . The proofs use elementary tools, such as rescaling or comparison arguments.
keywords
- blow-up; blow-up rates; fractional laplacian