, Volume 100, Issue 4, pp 361-367
Date: 10 Apr 2013

Gradient blowup rate for a viscous Hamilton–Jacobi equation with degenerate diffusion

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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.

This work was supported by the Fundamental Research Funds for the Central Universities of China and by the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry.