Gradient blowup solutions of a semilinear parabolic equation with exponential source

Zhengce Zhang; Yanyan Li

doi:10.3934/cpaa.2013.12.269

Article Contents

2013, Volume 12, Issue 1: 269-280. Doi: 10.3934/cpaa.2013.12.269

This issue Previous Article Behaviour of $p$--Laplacian problems with Neumann boundary conditions when $p$ goes to 1 Next Article On the structure of the global attractor for infinite-dimensional non-autonomous dynamical systems with weak convergence

Gradient blowup solutions of a semilinear parabolic equation with exponential source

Zhengce Zhang^1, and
Yanyan Li^2,

1.
College of Science, Xi’an Jiaotong University, Xi’an, 710049
2.
School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, 710049

Received: May 31, 2011

Revised: September 30, 2011

Published: December 2012

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Abstract

In this paper, we consider the N-dimensional semilinear parabolic equation $ u_t=\Delta u+e^{|\nabla u|}$, for which the spatial derivative of solutions becomes unbounded in finite (or infinite) time while the solutions themselves remain bounded. We establish estimates of blowup rate as well as lower and upper bounds for the radial solutions. We prove that in this case the blowup rate does not match the one obtained by the rescaling method.

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Mathematics Subject Classification: Primary: 35K05, 35K35; Secondary: 35B40.

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