I need to prove the Observability Inequality $$\|\varphi(0)\|_{L^2(\Omega)} \leq C \int\int_{O \times (0, T)} |\varphi^2| \; dx dt$$ from Carleman's Inequality for the heat equation, $- \varphi_t - \Delta \varphi = 0$. Would someone tell me a book or article that has proof of this?
2026-03-25 08:07:35.1774426055
Observability Inequality from the Carleman's Inequality
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