Heat Equation with Dynamical Boundary Conditions of Reactive Type
Juan Luis Vázquez, Enzo Vitillaro · Communications in Partial Differential Equations · 2008
The aim of this paper is to study the initial boundary problem where Ω is a bounded regular open domain in ℝN (N ≥ 1), Γ = ∂Ω, ν is the outward normal to Ω, and k < 0. In particular we prove that the problem is ill-posed when N ≥ 2, while it is well-posed in dimension N = 1. Moreover we carefully study the case when Ω is a ball in ℝN. As a byproduct we give several results on the elliptic eigenvalue problem