2016 Elsevier Inc. We study the behavior for t small and positive of C2,1 nonnegative solutions u(x,t) and v(x,t) of the system 0utuv0vtvuin(0,1), where and are nonnegative constants and is an open subset of Rn, n1. We provide optimal conditions on and such that solutions of this system satisfy pointwise bounds in compact subsets of as t0+. Our approach relies on new pointwise bounds for nonlinear heat potentials which are the parabolic analog of similar bounds for nonlinear Riesz potentials.
Journal of Functional Analysis
- Partial Differential Inequalities
- Heat Potential Estimate
- Pointwise Bound
- Parabolic System