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| We address a singular parabolic equation of the form $\theta_t + \Delta \theta^{-1} = 0$ on a smooth bounded domain $\Omega\subset {\bf R}^3$. The equation is complemented with a dynamic boundary condition of the form $\theta_t - \Delta_{\partial\Omega} \theta = \partial_\nu \theta^{-1}$ on $\partial\Omega$, where $\Delta_{\partial\Omega}$ is the Laplace-Beltrami operator and $\nu$ is the outer normal unit vector to $\partial \Omega$. We discuss existence, uniqueness, and regularity of solutions for the initial-value problem for this equation. |
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