Moving gradient singularity for the evolutionary p-Laplace equation

2024/11/01 by Erik Lindgren, Lindgren, Erik, Jin Takahashi +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.2411.00993

openalex publication_date 2024/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We consider the evolutionary p-Laplace equation in ℝⁿ. For p>n, we construct a solution u with a moving gradient singularity in the sense that |∇ u(x,t)|→ ∞ for each t as x→ξ(t), where ξ:[0,∞)→ℝⁿ is a given curve.

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