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Results tagged with parabolic-pde
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user 57856
Questions about partial differential equations of parabolic type. Often used in combination with the top-level tag ap.analysis-of-pdes.
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answer
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Uniqueness of weak solutions of a heat equation
Let $M$ be a smooth compact closed manifold.
Let $u \in H^1(0,T;H^{-1}(M)) \cap L^2(0,T;H^1(M))$ be a solution of
$$u_t - \Delta u - u = 0$$
$$u(0)=u(T)$$
satisfying $\int_M u(t) = 0$ for all $t$. Is …
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