The aim of this paper is to study the initial boundary problem u_t- Delta u=0 in (0,infty)xΩ, u_t = ku_ν on (0,infty)xΓ, u(0,x) = u_0(x) on Ω where Ω is a bounded regular open domain in R^N (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 R^N. As a byproduct we give several results on the related elliptic eigenvalue problem.
Heat equation with dynamical boundary conditions of reacting type
VITILLARO, Enzo
2008
Abstract
The aim of this paper is to study the initial boundary problem u_t- Delta u=0 in (0,infty)xΩ, u_t = ku_ν on (0,infty)xΓ, u(0,x) = u_0(x) on Ω where Ω is a bounded regular open domain in R^N (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 R^N. As a byproduct we give several results on the related elliptic eigenvalue problem.File in questo prodotto:
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