Some nonexistence results for higherorder evolution inequalities in conelike domains
Author:
Gennady G. Laptev
Journal:
Electron. Res. Announc. Amer. Math. Soc. 7 (2001), 8793
MSC (2000):
Primary 35G25; Secondary 35R45, 35K55, 35L70
DOI:
https://doi.org/10.1090/S1079676201000981
Published electronically:
October 15, 2001
MathSciNet review:
1856890
Fulltext PDF Free Access
Abstract  References  Similar Articles  Additional Information
Abstract: Nonexistence of global (positive) solutions of semilinear higherorder 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}\operatorname{div} (x^\alpha Du)\ge u^q \end{equation*} with $k=1,2,\dots$, in conelike 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
Received by editor(s):
April 7, 2001
Published electronically:
October 15, 2001
Additional Notes:
The author was supported in part by RFBR Grant #010100884.
Communicated by:
Guido Weiss
Article copyright:
© Copyright 2001
American Mathematical Society