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

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• 作者：Marius Ghergu^a ; ^{marius.ghergu@ucd.ie} ; Steven D. Taliaferro^b ; ^{stalia@math.tamu.edu}
• 关键词：35B09 ; 35B33 ; 35B44 ; 35B45 ; 35K40 ; 35R45
• 刊名：Journal of Functional Analysis
• 出版年：2017
• 出版时间：15 February 2017
• 年：2017
• 卷：272
• 期：4
• 页码：1301-1339
• 全文大小：578 K
• 卷排序：272

文摘

We study the behavior for t   small and positive of C2,1C2,1 nonnegative solutions u(x,t)u(x,t) and v(x,t)v(x,t) of the system0≤ut−Δu≤vλ0≤vt−Δv≤uσ in Ω×(0,1), where λ and σ   are nonnegative constants and Ω is an open subset of RnRn, n≥1n≥1. We provide optimal conditions on λ and σ   such that solutions of this system satisfy pointwise bounds in compact subsets of Ω as t→0+t→0+. Our approach relies on new pointwise bounds for nonlinear heat potentials which are the parabolic analog of similar bounds for nonlinear Riesz potentials.