# On Blow up at Space Infinity for Semilinear Heat Equations

Preprint Series # 670
Giga, Yoshikazu and Umeda, Noriaki On Blow up at Space Infinity for Semilinear Heat Equations. (2004);

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## Abstract

A 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 $v(0)=M$.

Item Type: Preprint 35-xx PARTIAL DIFFERENTIAL EQUATIONS 449