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Proceedings of the American Mathematical Society

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

 

 

Uniqueness for singular backward parabolic inequalities


Author: Alan V. Lair
Journal: Proc. Amer. Math. Soc. 98 (1986), 56-60
MSC: Primary 35K15; Secondary 35K20, 35R45
DOI: https://doi.org/10.1090/S0002-9939-1986-0848875-9
MathSciNet review: 848875
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Abstract: We prove that the only solution of the partial differential inequality

$\displaystyle {\left( {{u_t} + \sum\limits_{i = 1}^n {\left[ {{u_{{x_i}}}_{{x_i... ...} \right]} } \right)^2} \leqslant c\left[ {{u^2} + \vert{u_x}{\vert^2}} \right]$

on a bounded region with homogeneous initial and boundary conditions is the trivial one.

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DOI: https://doi.org/10.1090/S0002-9939-1986-0848875-9
Article copyright: © Copyright 1986 American Mathematical Society