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.

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. 
@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/}
}
TY  - JOUR
AU  - R. Ya. Glagoleva
TI  - A~sufficient condition for the existence of a~``dead zone'' for solutions of degenerate semilinear parabolic equations and inequalities
JO  - Matematičeskie zametki
PY  - 1996
SP  - 824
EP  - 831
VL  - 60
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_1996_60_6_a3/
LA  - ru
ID  - MZM_1996_60_6_a3
ER  - 
%0 Journal Article
%A R. Ya. Glagoleva
%T A~sufficient condition for the existence of a~``dead zone'' for solutions of degenerate semilinear parabolic equations and inequalities
%J Matematičeskie zametki
%D 1996
%P 824-831
%V 60
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_1996_60_6_a3/
%G ru
%F MZM_1996_60_6_a3
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/

[1] Diaz J. I., Nonlinear Partial Equations and Free Boundaries. V. 1. Elliptic Equations, Research Notes in Math., 106, Pitman, London, 1988

[2] Chipot M., Variational Inequalities and Flow in Pourpes Media, Appl. Math. Sci., 52, Springer-Verlag, Berlin, 1984 | MR | Zbl

[3] Chistyakov V. V., “O nekotorykh kachestvennykh svoistvakh reshenii nedivergentnogo polulineinogo parabolicheskogo uravneniya vtorogo poryadka”, UMN, 41:5 (1986), 199–210 | MR

[4] Chistyakov V. V., O svoistvakh polulineinykh parabolicheskikh uravnenii vtorogo poryadka, Tr. sem. im. I. G. Petrovskogo, 15, Izd-vo Mosk. un-ta, M., 1990

[5] Kondratev V. A., Landis E. M., “Polulineinye uravneniya vtorogo poryadka s neotritsatelnoi kharakteristicheskoi formoi”, Matem. zametki, 44:4 (1988), 457–468 | MR | Zbl

[6] Landis E. M., “Some properties of the solution of degenerating semilinear elliptic inequalities”, Russian J. Math. Phys., 1:4 (1993), 483–494 | MR | Zbl

[7] Landis E. M., Uravneniya vtorogo poryadka ellipticheskogo i parabolicheskogo tipov, Nauka, M., 1971