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Nonexistence results for higher-order evolution partial differential inequalities

Author: Gennady G. Laptev
Journal: Proc. Amer. Math. Soc. 131 (2003), 415-423
MSC (2000): Primary 35G25; Secondary 35R45, 35K55, 35L70
Published electronically: September 17, 2002
MathSciNet review: 1933332
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Abstract: Nonexistence of global solutions to semilinear higher-order (with respect to $t$) evolution partial differential inequalities $u^{(k)}_t-\Delta u\ge \vert x\vert^\sigma \vert u\vert^q$with $k=1,2,\dots$ in the complement of a ball is studied. The critical exponents $q^*$are found and the nonexistence results are proved for $1<q\le q^*$. The corresponding results for $k=1$ (parabolic problem) are sharp.

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Additional Information

Gennady G. Laptev
Affiliation: Department of Function Theory, Steklov Mathematical Institute, Gubkina str. 8, Moscow, Russia

Received by editor(s): June 10, 2001
Published electronically: September 17, 2002
Additional Notes: The author was supported in part by INTAS project 00-0136 and RFBR Grant #01-01-00884.
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2002 American Mathematical Society