A Triviality Result for Semilinear Parabolic Equations

2020/07/15 by Giovanni Catino, Catino, Giovanni, Daniele Castorina +3
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2007.07655

openalex publication_date 2020/07/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show a triviality result for "pointwise" monotone in time, bounded "eternal" solutions of the semilinear heat equation u_t=Δu + |u|^p on complete Riemannian manifolds of dimension n ≥ 5 with nonnegative Ricci tensor, when p is smaller than the critical Sobolev exponent (n+2)/(n-2).

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