Heat equation with dynamical boundary conditions of reactive–diffusive type

This paper deals with the heat equation posed in a bounded regular domain Ω of (N 2) coupled with a dynamical boundary condition of reactive–diffusive type. In particular we study the problem where u=u(t,x), t 0, x Ω, Γ=∂Ω, Δ=Δx denotes the Laplacian operator with respect to the space variable, while ΔΓ denotes the Laplace–Beltrami operator on Γ, ν is the outward normal to Ω, and k and l are given real constants, l>0. Well-posedness is proved for data u0 H1(Ω) such that u0Γ H1(Γ). We also study higher regularity of the solution.