Geodesic
A~sufficient condition for the existence of a~``dead zone'' for solutions of degenerate semilinear parabolic equations and inequalities
Matematičeskie zametki, Tome 60 (1996) no. 6, pp. 824-831

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We consider the solutions of degenerate parabolic equations and inequalities of the form $Lu-u_t=|u|^q\operatorname{sgn}u$ and $\operatorname{sgn}u(Lu-u_t)-|u|^q\ge0$, $0$, with the elliptic operator $L$ in divergent or nondivergent form. We establish a dependence of the maximum modulus of the solution on the domain and on the equation (inequality) such that this dependence guarantees the existence of a “dead zone” of the solution. In this case, the character of degeneracy is unessential. 
@article{MZM_1996_60_6_a3,
     author = {R. Ya. Glagoleva},
     title = {A~sufficient condition for the existence of a~``dead zone'' for solutions of degenerate semilinear parabolic equations and inequalities},
     journal = {Matemati\v{c}eskie zametki},
     pages = {824--831},
     publisher = {mathdoc},
     volume = {60},
     number = {6},
     year = {1996},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1996_60_6_a3/}
}
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R. Ya. Glagoleva. A~sufficient condition for the existence of a~``dead zone'' for solutions of degenerate semilinear parabolic equations and inequalities. Matematičeskie zametki, Tome 60 (1996) no. 6, pp. 824-831. http://geodesic.mathdoc.fr/item/MZM_1996_60_6_a3/