Abstract

This paper is concerned with the gradient blowup rate for the one-dimensional p-Laplacian parabolic equation \({u_t=(|u_x|^{p-2} u_x)_x +|u_x|^q}\) with q > p > 2, for which the spatial derivative of solutions becomes unbounded in finite time while the solutions themselves remain bounded. We establish the blowup rate estimates of lower and upper bounds and show that in this case the blowup rate does not match the self-similar one.

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