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On the existence of solutions of the Cauchy problem for porous medium equations with radon measure as initial data

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  • For any nonnegative Radon measure $\mu$, we prove the existence of solutions for the Cauchy problem:

    $ 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.

    Mathematics Subject Classification: 76S05, 35K10.


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