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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Log-log convexity and backward uniqueness
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by Igor Kukavica PDF
Proc. Amer. Math. Soc. 135 (2007), 2415-2421 Request permission

Abstract:

We study backward uniqueness properties for equations of the form \begin{equation*} u’ + A u = f. \end{equation*} Under mild regularity assumptions on $A$ and $f$, it is shown that $u(0)=0$ implies $u(t)=0$ for $t<0$. The argument is based on $\alpha$-log and log-log convexity. The results apply to mildly nonlinear parabolic equations and systems with rough coefficients and the 2D Navier-Stokes system.
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Additional Information
  • Igor Kukavica
  • Affiliation: Department of Mathematics, University of Southern California, Los Angeles, California 90089
  • MR Author ID: 314775
  • Email: kukavica@usc.edu
  • Received by editor(s): November 1, 2004
  • Received by editor(s) in revised form: August 30, 2005
  • Published electronically: March 14, 2007
  • Additional Notes: The author was supported in part by the NSF grant DMS-0306586
  • Communicated by: David S. Tartakoff
  • © Copyright 2007 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 135 (2007), 2415-2421
  • MSC (2000): Primary 35B42, 35B41, 35K55, 35K15, 35G20
  • DOI: https://doi.org/10.1090/S0002-9939-07-08991-5
  • MathSciNet review: 2302562