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Keywords:
quasilinear heat equation; total blow-up; blow-up only at space infinity
quasilinear heat equation; total blow-up; blow-up only at space infinity
Summary:
We consider solutions of quasilinear equations $u_{t}=\Delta u^{m} + u^{p}$ in $\mathbb R^{N}$ with the initial data $u_{0}$ satisfying $0 < u_{0}< M$ and $\lim _{|x|\to \infty }u_{0}(x)=M$ for some constant $M>0$. It is known that if $0<m<p$ with $p>1$, the blow-up set is empty. We find solutions $u$ that blow up throughout $\mathbb R^{N}$ when $m>p>1$.
References:
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