Sign-changing blowing-up solutions for the critical nonlinear heat equation

2018/10/31 by Manuel del Pino, del Pino, Manuel, Monica Musso +5 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1811.00039

openalex publication_date 2018/10/31 · openalex created_date 2018/11/09 · openalex updated_date 2026/07/28

Abstract

Let Ω be a smooth bounded domain in ℝⁿ and denote the regular part of the Green's function on Ω with Dirichlet boundary condition as H(x,y). Assume that q ∈ Ω and n≥ 5. We prove that there exists an integer k₀ such that for any integer k≥ k₀ there exist initial data u₀ and smooth parameter functions ξ(t)→ q, 0

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