2011/03/31 by Rolando Magnanini, Shigeru Sakaguchi, Magnanini, Rolando +1
Computer Science · Mathematics · #35B06 #35K20 #35K55 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #Primary 35K05 #Secondary 35K15 #math.AP #msc:35B06 #msc:35K05 #msc:35K15 #msc:35K20 #msc:35K55
paper · pdf · doi:10.48550/arxiv.1103.6229
16 pages; no figures. Added an appendix with the proof of Theorem B, to make the paper self-contained. Some other minor modifications
openalex publication_date 2011/03/31 · arxiv created 2011/07/13 · arxiv updated 2011/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider nonlinear diffusion equations of the form ∂t u= Δϕ(u) in \mathbb RN with N ≥ 2. When ϕ(s) ≡ s, this is just the heat equation. Let Ω be a domain in \mathbb RN, where ∂Ω is bounded and ∂Ω= ∂ (\mathbb RN∖ Ω). We consider the initial-boundary value problem, where the initial value equals zero and the boundary value equals 1, and the Cauchy problem where the initial data is the characteristic function of the set Ωc = \mathbb RN∖ Ω. We settle the boundary regularity issue for the characterization of the sphere as a stationary level surface of the solution u: no regularity assumption is needed for ∂Ω.