Initial Pointwise Bounds and Blow-up for Parabolic Choquard-Pekar Inequalities | Academic Article individual record
abstract

We study the behavior as t 0+ of nonnegative functions (Equation presented) satisfying the parabolic Choquard-Pekar type inequalities (Equation presented) where (0,n + 2), > 0, and 0 are constants, is the heat kernel, and is the convolution operation in n (0,1). We provide optimal conditions on , , and such that nonnegative solutions u of (0.1),(0.2) satisfy pointwise bounds in compact subsets of B1 (0) as t 0+. We obtain similar results for nonnegative solutions of (0.1),(0.2) when /n in (0.2) is replaced with the fundamental solution , of the fractional heat operator (/t - )/2.

publication outlet

Discrete & Continuous Dynamical Systems - A

author list (cited authors)
D. Taliaferro, S.
publication date
2017
keywords
  • Choquard
  • Heat Potential
  • Parabolic
  • Pointwise Bound
  • Initial Blow-up
  • Nonlocal
citation count

1

identifier
293595SE
Digital Object Identifier (DOI)
start page
5211
end page
5252
volume
37
issue
10