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Mat. Zametki, 1996, Volume 60, Issue 6, Pages 824–831 (Mi mz1900)  

A sufficient condition for the existence of a “dead zone” for solutions of degenerate semilinear parabolic equations and inequalities

R. Ya. Glagoleva

Moscow Aviation Institute

Abstract: We consider the solutions of degenerate parabolic equations and inequalities of the form $Lu-u_t=|u|^q\operatorname{sgn}u$ and $\operatorname{sgn}u(Lu-u_t)-|u|^q\ge0$, $0<q<1$, 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.

DOI: https://doi.org/10.4213/mzm1900

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English version:
Mathematical Notes, 1996, 60:6, 622–628

Bibliographic databases:

UDC: 517.946
Received: 20.10.1992
Revised: 19.09.1995

Citation: R. Ya. Glagoleva, “A sufficient condition for the existence of a “dead zone” for solutions of degenerate semilinear parabolic equations and inequalities”, Mat. Zametki, 60:6 (1996), 824–831; Math. Notes, 60:6 (1996), 622–628

Citation in format AMSBIB
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\pages 824--831
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\jour Math. Notes
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\pages 622--628
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