Boundary singular solutions of a class of equations with mixed absorption-reaction

2020/07/31 by Marie-Françoise Bidaut-Veron, Bidaut-Veron, Marie-Françoise, Marta Garcia-Huidobro +3
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.2007.16097

44 pages, 26 ref

arxiv created 2022/01/24 · arxiv updated 2022/01/25

Abstract

We study properties of positive functions satisfying (E) --Δu + u p -- M |∇u| q = 0 is a domain Ω or in R N + when p > 1 and 1 < q < minp, 2. We concentrate our research on the solutions of (E) vanishing on the boundary except at one point. This analysis depends on the existence of separable solutions in R N +. We consruct various types of positive solutions with an isolated singularity on the boundary. We also study conditions for the removability of compact boundary sets and the Dirichlet problem associated to (E) with a measure for boundary data.

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