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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

Abstract:

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: laptev@home.tula.net
  • 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: https://doi.org/10.1090/S0002-9939-02-06665-0
  • MathSciNet review: 1933332