Geodesic
Behaviour of solutions of certain quasilinear parabolic equations with power-type non-linearities
Sbornik. Mathematics, Tome 191 (2000) no. 3, pp. 341-358

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The Cauchy problem with non-negative continuous initial function for the equation $$ u_t=\Delta u^m-u^p, \qquad (x,t)\in S=\mathbb R^N\times\mathbb R_+, $$ is considered for $0$, $p$. For generalized solutions of this problem with initial data increasing at infinity several results on their behaviour as $t\to\infty$ are established. 
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     author = {A. L. Gladkov},
     title = {Behaviour of solutions of certain quasilinear parabolic equations with power-type non-linearities},
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A. L. Gladkov. Behaviour of solutions of certain quasilinear parabolic equations with power-type non-linearities. Sbornik. Mathematics, Tome 191 (2000) no. 3, pp. 341-358. http://geodesic.mathdoc.fr/item/SM_2000_191_3_a2/