Initial Pointwise Bounds and Blow-up for Parabolic Choquard-Pekar Inequalities Academic Article uri icon

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.

published proceedings

  • Discrete & Continuous Dynamical Systems - A

author list (cited authors)

  • D. Taliaferro, S.

citation count

  • 1

complete list of authors

  • D. Taliaferro, Steven

publication date

  • January 2017