Heat equation with an exponential nonlinear boundary condition in the half space

We consider the initial-boundary value problem for the heat equation in the half space with an exponential nonlinear boundary condition. We prove the existence of global-in-time solutions under the smallness condition on the initial data in the Orlicz space expL*2(R^N_+). Furthermore, we derive decay estimates and the asymptotic behavior for small global-in-time solutions.