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- W2322941824 abstract "This paper is concerned with the critical exponents for the porous medium equation <p align=center> $u_{t}=triangle u^m+a(x)u^p, (x,t)in R^Ntimes (0,T), $ <p align=left class=times> where $m>1, p>0,$ and the function $a(x)geq 0$ has a compact support. Suppose the space dimension $Ngeq 2$, we prove that the global exponent $p_0$ and the Fujita type exponent $p_c$ are both $m$: if $0 < p < m$ every solution is global in time, if $ p = m $ all the solutions blow up and if $p > m$ both the blowing up solutions and the global solutions exist. While for the one-dimensional case, it is proved $p_0=frac{m+1}{2} < m+1 = p_c$ by [E. Ferreira, A. Pablo, J. Vazquez, <em>Classification of blow-up with nonlinear diffusion and localized reaction</em>, J. Diff. Eqns., 231(2006) 195-211]." @default.
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- W2322941824 date "2012-01-01" @default.
- W2322941824 modified "2023-09-26" @default.
- W2322941824 title "On the critical exponents for porous medium equation with a localized reaction in high dimensions" @default.
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- W2322941824 doi "https://doi.org/10.3934/cpaa.2012.11.649" @default.
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