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}
}

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.