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arXiv · 2303.04713

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

Elie Abdo·Weinan Wang
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Abstract

We consider the inhomogeneous heat equation on the half-space $\mathbb R_{+}^{d}$ 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 in [10].

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Elie Abdo, Weinan Wang. 2023-03-08. On the space-time analyticity of the inhomogeneous heat equation on the half space with Neumann boundary conditions. https://arxiv.org/abs/2303.04713

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