Pointwise bounds and blow-up for systems of semilinear parabolic inequalities and nonlinear heat potential estimates | Academic Article individual record
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.

publication outlet

Journal of Functional Analysis

author list (cited authors)
Ghergu, M., & Taliaferro, S. D.
publication date
2017
publisher
Elsevier bv Publisher
keywords
  • Partial Differential Inequalities
  • Heat Potential Estimate
  • Pointwise Bound
  • Parabolic System
citation count

1

identifier
171176SE
Digital Object Identifier (DOI)
start page
1301
end page
1339
volume
272
issue
4