On the space-time analyticity of the inhomogeneous heat equation on the half space with Neumann boundary conditions

We consider the inhomogeneous heat equation on the half-space R+d with Neumann boundary conditions. We prove a space-time Gevrey regularity of the solution, with a radius of analyticity uniform up to the boundary of the half-space. We also address the case of homogeneous Robin boundary conditions. Our results generalize the case of homogeneous Dirichlet boundary conditions established by Kukavica and Vicol [A direct approach to Gevrey regularity on the half-space. In: Partial differential equations in fluid mechanics. Cambridge: Cambridge Univ. Press; 2018. p. 268–288. (London math. soc. lecture note ser.; vol. 452).].