Pointwise bounds and blow-up for systems of semilinear parabolic inequalities and nonlinear heat potential estimates Academic Article uri icon

abstract

  • 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.

published proceedings

  • Journal of Functional Analysis

author list (cited authors)

  • Ghergu, M., & Taliaferro, S. D.

citation count

  • 1

complete list of authors

  • Ghergu, Marius||Taliaferro, Steven D

publication date

  • February 2017