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

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.

authors

• Taliaferro, Steven

published proceedings

• JOURNAL OF FUNCTIONAL ANALYSIS

author list (cited authors)

• Ghergu, M., & Taliaferro, S. D.

citation count

• 2

complete list of authors

• Ghergu, Marius||Taliaferro, Steven D

publication date

• January 2017

publisher

• Elsevier  Publisher

published in

• Journal of Functional Analysis  Journal

keywords

• Heat Potential Estimate
• Parabolic System
• Partial Differential Inequalities
• Pointwise Bound

Digital Object Identifier (DOI)

• 10.1016/j.jfa.2016.12.010

start page

• 1301

end page

• 1339

volume

• 272

issue

• 4

URL

• http%3A%2F%2Fdx.doi.org%2F10.1016%2Fj.jfa.2016.12.010