Geodesic
Fujita type theorems for quasilinear parabolic equations
Sbornik. Mathematics, Tome 195 (2004) no. 4, pp. 459-478

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This work deals with the Cauchy problem for a parabolic equation with a double non-linearity of the following type: $$ u_t=\operatorname{div}(u^\alpha|Du|^{m-1}Du)+u^p, $$ where $0$. Existence and non-existence results for global solutions of this problem with initial conditions that slowly decay to zero are established. 
@article{SM_2004_195_4_a0,
     author = {N. V. Afanasieva and A. F. Tedeev},
     title = {Fujita type theorems for quasilinear parabolic equations},
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     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2004_195_4_a0/}
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N. V. Afanasieva; A. F. Tedeev. Fujita type theorems for quasilinear parabolic equations. Sbornik. Mathematics, Tome 195 (2004) no. 4, pp. 459-478. http://geodesic.mathdoc.fr/item/SM_2004_195_4_a0/