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Transactions of the American Mathematical Society

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

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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The heat equation with a singular potential
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by Pierre Baras and Jerome A. Goldstein PDF
Trans. Amer. Math. Soc. 284 (1984), 121-139 Request permission

Abstract:

Of concern is the singular problem $\partial u/\partial t = \Delta u + (c/|x{|^2}) u + f(t,x), u(x,0) = u_{0}(x)$, and its generalizations. Here $c \geqslant 0,x \in {{\mathbf {R}}^N},t > 0$, and $f$ and ${u_0}$ are nonnegative and not both identically zero. There is a dimension dependent constant ${C_{\ast } }(N)$ such that the problem has no solution for $c > {C_{\ast } }(N)$. For $c \leqslant {C_{\ast } }(N)$ necessary and sufficient conditions are found for $f$ and ${u_0}$ so that a nonnegative solution exists.
References
    P. Baras, in preparation.
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Additional Information
  • © Copyright 1984 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 284 (1984), 121-139
  • MSC: Primary 35K05; Secondary 60J65
  • DOI: https://doi.org/10.1090/S0002-9947-1984-0742415-3
  • MathSciNet review: 742415