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MR539218 35K15 (35K55)
Brézis, Haïm; Crandall, Michael G. Uniqueness of solutions of the initial-value problem for $u\sb{t}-\Delta \varphi (u)=0$. J. Math. Pures Appl. (9) 58 (1979), no. 2, 153–163.
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