Archiv der Mathematik

, Volume 100, Issue 4, pp 361–367

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

Authors

    • School of Mathematics and StatisticsXi’an Jiaotong University
Article

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

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.

Mathematics Subject Classification (2010)

35B3535K5835B20

Keywords

Degenerate diffusionGradient blowup rateHamilton–Jacobi equation

Copyright information

© Springer Basel 2013