Classification of local asymptotics for solutions to heat equations with inverse-square potentials

2010/02/18 by Veronica Felli, Ana Primo, Felli, Veronica +1
Mathematics · #35B40 #35K58 #35K67 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1002.3566

openalex publication_date 2010/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Asymptotic behavior of solutions to heat equations with spatially singular inverse-square potentials is studied. By combining a parabolic Almgren type monotonicity formula with blow-up methods, we evaluate the exact behavior near the singularity of solutions to linear and subcritical semilinear parabolic equations with Hardy type potentials. As a remarkable byproduct, a unique continuation property is obtained.

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