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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.

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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Uniqueness for singular backward parabolic inequalities
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by Alan V. Lair PDF
Proc. Amer. Math. Soc. 98 (1986), 56-60 Request permission

Abstract:

We prove that the only solution of the partial differential inequality \[ {\left ( {{u_t} + \sum \limits _{i = 1}^n {\left [ {{u_{{x_i}}}_{{x_i}} + \left ( {\frac {{{k_i}}}{{{x_i}}}} \right ){u_{{x_i}}}} \right ]} } \right )^2} \leqslant c\left [ {{u^2} + |{u_x}{|^2}} \right ]\] on a bounded region with homogeneous initial and boundary conditions is the trivial one.
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Additional Information
  • © Copyright 1986 American Mathematical Society
  • 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