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 RN (N⩾2) coupled with a dynamical boundary condition of reactive–diffusive type. In particular we study the problem View the MathML source 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 u0|Γ∈H1(Γ). We also study higher regularity of the solution.