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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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Convergence of sequences of semigroups of nonlinear operators with an application to gas kinetics
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by Thomas G. Kurtz PDF
Trans. Amer. Math. Soc. 186 (1973), 259-272 Request permission

Abstract:

Let ${A_1},{A_2}, \cdots$ be dissipative sets that generate semigroups of nonlinear contractions ${T_1}(t),{T_2}(t) \cdots$ Conditions are given on $\{ {A_n}\}$ which imply the existence of a limiting semigroup T(t). The results include types of convergence besides strong convergence. As an application, it is shown that solutions of the pair of equations \[ {u_t} = - \alpha {u_x} + {\alpha ^2}({v^2} - {u^2})\] and \[ {v_t} = \alpha {v_x} + {\alpha ^2}({u^2} - {v^2}),\] $\alpha$ a constant, approximate the solutions of \[ {u_t} = 1/4({d^2}/d{x^2}) \log u\] as $\alpha$ goes to infinity.
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Additional Information
  • © Copyright 1973 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 186 (1973), 259-272
  • MSC: Primary 47H15
  • DOI: https://doi.org/10.1090/S0002-9947-1973-0336482-1
  • MathSciNet review: 0336482