The blow-up properties of solutions to semilinear heat equations with nonlinear boundary conditions

@article{Lin1999TheBP,
  title={The blow-up properties of solutions to semilinear heat equations with nonlinear boundary conditions},
  author={Zhigui Lin and M. Wang},
  journal={Zeitschrift f{\"u}r angewandte Mathematik und Physik ZAMP},
  year={1999},
  volume={50},
  pages={361-374}
}
  • Zhigui Lin, M. Wang
  • Published 1999
  • Mathematics
  • Zeitschrift für angewandte Mathematik und Physik ZAMP
Abstract. This paper deals with the blow-up properties of solutions to semilinear heat equation $u_t-u_{xx}=u^p \text{ in }(0,1)\times(0,T)$ with the nonlinear boundary conditions $u_x(0,t)=0,u_x(1,t)=u^q\text{ on }[0,T)$. The necessary and sufficient conditions for the solution to have a finite time blow-up and the exact blow-up rates are established. It is also proved that the blow-up will occur only at the boundary x = 1.  
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