Solutions with time-dependent singular sets for the heat equation with absorption

2017/12/17 by Jin Takahashi, Takahashi, Jin, Hikaru Yamamoto +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1712.06065

openalex publication_date 2017/12/17 · openalex created_date 2018/01/05 · openalex updated_date 2026/07/28

Abstract

We consider the heat equation with a superlinear absorption term ∂_t u-Δu= -u^p in ℝⁿ and study the existence and nonexistence of nonnegative solutions with an m-dimensional time-dependent singular set, where n-m≥ 3. First, we prove that if p≥ (n-m)/(n-m-2), then there is no singular solution. We next prove that, if 1

Citations

• A Compactness Theorem for the Second Fundamental Form

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