Archiv der Mathematik

, Volume 100, Issue 4, pp 361–367

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


    • School of Mathematics and StatisticsXi’an Jiaotong University

DOI: 10.1007/s00013-013-0505-4

Cite this article as:
Zhang, Z. Arch. Math. (2013) 100: 361. doi:10.1007/s00013-013-0505-4


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.

Mathematics Subject Classification (2010)



Degenerate diffusionGradient blowup rateHamilton–Jacobi equation

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© Springer Basel 2013