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 α ∈ (0,n + 2), λ > 0, and σ ≥ 0 are constants, Φ is the heat kernel, and ∗ is the convolution operation in ℝn × (0,1). We provide optimal conditions on α, λ, and σ 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 Φα/n in (0.2) is replaced with the fundamental solution Φα, of the fractional heat operator (δ/δt - Δ)α/2.

author list (cited authors)

  • D. Taliaferro, S.

citation count

  • 1

publication date

  • January 2017