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Nonradial solvability structure of super-diffusive nonlinear parabolic equations

We study the solvability of the Cauchy problem for the nonlinear parabolic equation ∂u = div (u m-1 Δu) at when m 0, then there is no local solution of the initial value problem. On the other hand, if such an interval does not exist, then the initial value problem is locally solvable and the time of existence can be estimated explicitly.