On finite-time blow-up for a nonlocal parabolic problem arising from shear bands in metals

Zheng, Gao-Feng

doi:10.1090/S0002-9939-06-08925-8

On finite-time blow-up for a nonlocal parabolic problem arising from shear bands in metals
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by Gao-Feng Zheng PDF

Proc. Amer. Math. Soc. 135 (2007), 1487-1494 Request permission

Abstract:

Results on finite-time blow-up of solutions to the nonlocal parabolic problem \[ \begin {cases} u_t=\Delta u +\delta \dfrac {e^u}{\left (\int _{\Omega }e^{u}\right )^p} \ \ & \text {in $\Omega \times (0,T)$, $0<p<1$, $\delta >0$},\\ u(x,t)=0, & (x,t)\in \partial \Omega \times (0,T),\\ u(x,0)=u_0(x)\geqslant 0,& x\in \Omega \end {cases} \] are established. They extend some known results to higher dimensions.

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