Heat Equation with Dynamical Boundary Conditions of Reactive Type

@inproceedings{Vzquez2004HeatEW,
  title={Heat Equation with Dynamical Boundary Conditions of Reactive Type},
  author={Juan Luis V{\'a}zquez and ENZO VITILLARO},
  year={2004}
}
The aim of this paper is to study the initial and boundary value problem    ut −∆u = 0 in Q = (0,∞)× Ω, ut = kuν on [0,∞)× Γ, u(0, x) = u0(x) on Ω, 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 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… CONTINUE READING