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Existence and uniqueness of an elliptic equation coupled with a parabolic equation (mean cur...

Given a parabolic equation on a simply connected smooth domain $\Omega(t)$ with boundary $\Gamma(t)$ $$ \Delta u = 1 \quad on \quad \Omega(t) \\ \nabla u \cdot n + u = g \quad on \quad \Gamma(t) $$ (w …
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