Geodesic
Self-similar solutions of half-linear heat equation
Matematičeskoe modelirovanie, Tome 2 (1990) no. 3, pp. 63-74.

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For half-linear heat equation \[ u_t=\Delta u+u^{\beta}\tag{1} \] in $N$-dimentional space the domains of parameters $N$ and $\beta$ is found, where the equation (1) has $n$ different self-similar solutions developing in blow up regime. 
@article{MM_1990_2_3_a6,
     author = {L. A. Lepin},
     title = {Self-similar solutions of half-linear heat equation},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {63--74},
     publisher = {mathdoc},
     volume = {2},
     number = {3},
     year = {1990},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_1990_2_3_a6/}
}
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L. A. Lepin. Self-similar solutions of half-linear heat equation. Matematičeskoe modelirovanie, Tome 2 (1990) no. 3, pp. 63-74. http://geodesic.mathdoc.fr/item/MM_1990_2_3_a6/