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Breakdown of solutions to $\square u+u_t=|u|^{1+\alpha}$
On the existence of solutions of the Cauchy problem for porous medium equations with radon measure as initial data
| 1. | Graduate School of Information Sciences, Tohoku University, Aoba-ku, Sendai 980-77, Japan |
$ u_t =\Delta\phi(u)\qquad\text{in}\quad R^N\times(0,T);\qquad u(\cdot,0) =\mu(\cdot)\ge 0\quad \text{in}\quad R^N, $
where $\phi'(s)$ ~ $\log^m s$, $m<-1$, as $s\to\infty$. On the other hand, for the case $m\ge -1$, we give a sufficient condition for the solvability of the Cauchy problem.
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