Proceedings of the American Mathematical Society

Nonexistence results for higher-order evolution partial differential inequalities

Author(s): Gennady G. Laptev
Journal: Proc. Amer. Math. Soc. 131 (2003), 415-423.
MSC (2000): Primary 35G25; Secondary 35R45, 35K55, 35L70
Posted: September 17, 2002
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Abstract: Nonexistence of global solutions to semilinear higher-order (with respect to

) 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

are found and the nonexistence results are proved for $1<q\le q^*$ . The corresponding results for

(parabolic problem) are sharp.

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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 35G25, 35R45, 35K55, 35L70

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

DOI: 10.1090/S0002-9939-02-06665-0
PII: S 0002-9939(02)06665-0
Received by editor(s): June 10, 2001
Posted: 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 of article: Copyright 2002, American Mathematical Society

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