Blow-up rates for a fractional heat equation Articles uri icon

publication date

  • May 2021

start page

  • 2011

end page

  • 2018

issue

  • 5

volume

  • 149

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