On finite-time blow-up for a nonlocal parabolic problem arising from shear bands in metals
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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.References
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Additional Information
- Gao-Feng Zheng
- Affiliation: Department of Mathematics, Huazhong Normal University, Wuhan, People’s Republic of China
- Email: gfzheng76@yahoo.com.cn
- Received by editor(s): October 5, 2005
- Received by editor(s) in revised form: December 20, 2005
- Published electronically: November 27, 2006
- Communicated by: David S. Tartakoff
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 1487-1494
- MSC (2000): Primary 35K10, 35K57, 35K60
- DOI: https://doi.org/10.1090/S0002-9939-06-08925-8
- MathSciNet review: 2276658