On Blow up at Space Infinity for Semilinear Heat EquationsPreprint Series # 670
AbstractA nonnegative blowing up solution of the semilinear heat equation $u_t =\Delta u+u^p $ with $p>1$ is considered when initial data $u_0 $ satisfies \begin{eqnarray*} \lim_{x \to \infty } u_0 =M>0, \hspace{5mm} u_0 \le M \hspace{3mm} \mbox{ and } \hspace{3mm} u_0 \not\equiv M. \end{eqnarray*} It is shown that the solution blows up only at space infinity and that $\lim_{x\to \infty } u(x,t)$ is the solution of the ordinary differential equation $v_t =v^p $ with $v(0)=M$.
