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Feb 23, 2015 at 15:40 comment added Michael Renardy There is a rather extensive literature on parabolic equations with nonsmooth coefficients. The work of Ladyzhenskaya and Uraltseva is a good place to start searching.
Feb 23, 2015 at 15:28 comment added C_Al @Hachino Definitely more smooth than that, let's say $u_0 \in H^1(\Omega)$.
Feb 23, 2015 at 15:26 comment added Hachino What conditions do you put on your initial data ? If you allow Dirac measures, your conclusion does not hold.
Feb 23, 2015 at 13:39 history asked C_Al CC BY-SA 3.0