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 
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/
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     title = {A~sufficient condition for the existence of a~{\textquotedblleft}dead zone{\textquotedblright} for solutions of degenerate semilinear parabolic equations and inequalities},
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

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