Archiv der Mathematik

, Volume 100, Issue 4, pp 361–367

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



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)

35B35 35K58 35B20 


Degenerate diffusion Gradient blowup rate Hamilton–Jacobi equation 


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Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsXi’an Jiaotong UniversityXi’anPeople’s Republic of China

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