1988/08/31 by Shoshana Kamin, S. Kamin, Juan Luis Vázquez · 2 citations
Computer Science · Mathematics · Medicine · #Advanced Mathematical Modeling in Engineering #Applied mathematics #Calculus (dental) #Laplace operator #Mathematical analysis #Mathematics #Medicine #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics
paper · doi:10.4171/rmi/77
crossref issued 1988/08/31 · crossref published 1988/08/31 · crossref published-print 1988/08/31 · openalex publication_date 1988/08/31 · crossref created 2012/01/05 · crossref deposited 2025/07/31 · openalex created_date 2025/10/10 · crossref indexed 2026/08/05 · openalex updated_date 2026/08/06
We establish the uniqueness of fundamental solutions to the p -Laplacian equation \mathrm (PLE) ut = \mathrm div (|Du|p-2Du), p > 2, defined for x ∈ \mathbb RN , 0 < t < T . We derive from this result the asymptotic behaviour of nonnegative solutions with finite mass, i.e. such that u(\cdotp, t) ∈ L1(\mathbb RN) . Our methods also apply to the porous medium equation \mathrm (PME) ut = Δ (um), m > 1, giving new and simpler proofs of known results. We finally introduce yet another method of proving asymptotic results based on the idea of asymptotic radial symmetry. This method can be useful in dealing with more general equations.