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Transactions of the American Mathematical Society

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

 
 

 

Convergence of sequences of semigroups of nonlinear operators with an application to gas kinetics


Author: Thomas G. Kurtz
Journal: Trans. Amer. Math. Soc. 186 (1973), 259-272
MSC: Primary 47H15
DOI: https://doi.org/10.1090/S0002-9947-1973-0336482-1
Erratum: Trans. Amer. Math. Soc. 209 (1975), 442.
MathSciNet review: 0336482
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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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Keywords: Nonlinear semigroups, approximation, gas kinetics
Article copyright: © Copyright 1973 American Mathematical Society