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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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Nonexistence results for higher–order evolution partial differential inequalities
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by Gennady G. Laptev PDF
Proc. Amer. Math. Soc. 131 (2003), 415-423 Request permission


Nonexistence of global solutions to semilinear higher-order (with respect to $t$) evolution partial differential inequalities $u^{(k)}_t-\Delta u\ge |x|^\sigma |u|^q$ 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
  • Email:
  • 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
  • © Copyright 2002 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 131 (2003), 415-423
  • MSC (2000): Primary 35G25; Secondary 35R45, 35K55, 35L70
  • DOI:
  • MathSciNet review: 1933332