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Blowup rate estimates for the heat equation with a nonlinear gradient source term

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  • The gradient blowup rate of the equation $u_t = \Delta u + |\nabla u|^p$, where $p>2$, is studied. It is shown that the blowup rate will never match that of the self-similar variables. In the one space dimensional case when assumptions are made on the initial data so that the solution is monotonically increasing in time, the exact blowup rate is found.
    Mathematics Subject Classification: Primary: 35K55; Secondary: 35B35.


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