Classification of positive solutions of heat equation with supercritical absorption

2013/08/06 by Konstantinos T. Gkikas, Konstantinos Gkikas, Gkikas, Konstantinos +3
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #advanced mathematical theories #math.AP

paper · pdf · doi:10.48550/arxiv.1308.1361

openalex publication_date 2013/08/06 · arxiv created 2013/12/15 · arxiv updated 2013/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let q≥ 1+(2)/(N). We prove that any positive solution of (E) \prt_t u-\xD u+u^q=0 in ℝ^N×(0,∞) admits an initial trace which is a nonnegative Borel measure, outer regular with respect to the fine topology associated to the Bessel capacity C_(2)/(q),q' in \BBR^N (q'=q/q-1)) and absolutely continuous with respect to this capacity. If ν is a nonnegative Borel measure in \BBR^N with the above properties we construct a positive solution u of (E) with initial trace \gn and we prove that this solution is the unique \gs-moderate solution of (E) with such an initial trace. Finally we prove that every positive solution of (E) is \gs-moderate.

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