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Nonexistence of global (positive) solutions of semilinear higher-order evolution inequalities \begin{equation*} \frac{\partial^k u}{\partial t^k}-\Delta u^m\ge |u|^q,\quad \frac{\partial^k u}{\partial t^k}-\Delta u\ge |x|^\sigma u^q,\quad \frac{\partial^ku}{\partial t^k}-\text{\rm div}\, (|x|^\alpha Du)\ge u^q \end{equation*} with $k=1,2,\dots$, in cone-like domains is studied. The critical exponents $q^*$ are found and the nonexistence results are proved for $1 < q\le q^*$. Remark that the corresponding result for $k=1$ (parabolic problem) is sharp.

Copyright 2001 American Mathematical Society

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Article Info

• ERA Amer. Math. Soc. 07 (2001), pp. 87-93
• Publisher Identifier: S 1079-6762(01)00098-1
• 2000 Mathematics Subject Classification. Primary 35G25; Secondary 35R45, 35K55, 35L70
• Received by the editors April 7, 2001
• Posted on October 15, 2001
• Communicated by Guido Weiss
• Comments (When Available)

Gennady G. Laptev

Department of Function Theory, Steklov Mathematical Institute, Gubkina Street 8, Moscow, Russia

E-mail address: laptev@home.tula.net

The author was supported in part by RFBR Grant #01-01-00884.