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Some nonexistence results for higher-order evolution inequalities in cone-like domains

Author(s): Gennady G. Laptev
Journal: Electron. Res. Announc. Amer. Math. Soc. 7 (2001), 87-93.
MSC (2000): Primary 35G25; Secondary 35R45, 35K55, 35L70
Posted: October 15, 2001
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Abstract: Nonexistence of global (positive) solutions of semilinear higher-order evolution inequalities

\begin{displaymath}\frac{\partial^k u}{\partial t^k}-\Delta u^m\ge \vert u\vert^... ...\partial t^k}-\text{\rm div}\, (\vert x\vert^\alpha Du)\ge u^q \end{displaymath}

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.

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Additional Information:

Gennady G. Laptev
Affiliation: Department of Function Theory, Steklov Mathematical Institute, Gubkina Street 8, Moscow, Russia
Email: laptev@home.tula.net

DOI: 10.1090/S1079-6762-01-00098-1
PII: S 1079-6762(01)00098-1
Received by editor(s): April 7, 2001
Posted: October 15, 2001
Additional Notes: The author was supported in part by RFBR Grant #01-01-00884.
Communicated by: Guido Weiss
Copyright of article: Copyright 2001, American Mathematical Society

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