I cannot find the following equation $$u_t=u^2u_{xx}$$ anywhere in the literature. Could someone please point me in the direction of what's been published on this?
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3$\begingroup$ This is a nonlinear parabolic equation, with non strict parabolicity. Not much exists in the literature, many years ago we did some work on this kind of problem, which has some interesting features $\endgroup$– Piero D'AnconaCommented Oct 4, 2017 at 7:50
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$\begingroup$ @PieroD'Ancona I was able to find your paper, arpi.unipi.it/handle/11568/49107#.WdVdv1ftLIo useful for my application. Thank you. $\endgroup$– garserdt216Commented Oct 4, 2017 at 22:18
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