Global well-posedness of solutions to a class of heat equation under dynamical type boundary conditions

Purpose By employing the Galerkin approximation and a family of potential wells, we establish the existence of a global solution and finite-time blow-up under certain suitable conditions. Additionally, we provide results concerning the asymptotic behavior of certain solution with positive initial energy. Design/methodology/approach The authors used the Galerkin approximation method and potential-well method. Findings The authors established some results on the existence of a global solution, the finite time blow-up of solutions and the asymptotic behavior of certain solutions with positive initial energy. Originality/value This work generalizes several published works.