Geodesic
Total blow-up of a quasilinear heat equation with slow-diffusion for non-decaying initial data
Mathematica Bohemica, Tome 144 (2019) no. 3, pp. 287-297
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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 $01$, the blow-up set is empty. We find solutions $u$ that blow up throughout $\mathbb R^{N}$ when $m>p>1$.
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 $0$ with $p>1$, the blow-up set is empty. We find solutions $u$ that blow up throughout $\mathbb R^{N}$ when $m>p>1$.
DOI : 10.21136/MB.2018.0026-18
Classification : 35B44, 35K59
Keywords: quasilinear heat equation; total blow-up; blow-up only at space infinity 
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Ling, Amy Poh Ai; Shimojō, Masahiko. Total blow-up of a quasilinear heat equation with slow-diffusion for non-decaying initial data. Mathematica Bohemica, Tome 144 (2019) no. 3, pp. 287-297. doi: 10.21136/MB.2018.0026-18

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