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.
Discrete & Continuous Dynamical Systems - A
- Heat Potential
- Pointwise Bound
- Initial Blow-up