Asymptotic Expansions for Regularized State-Dependent Neutral Delay Equations

نویسندگان

  • Nicola Guglielmi
  • Ernst Hairer
چکیده

Singularly perturbed delay differential equations arising from the regularization of state dependent neutral delay equations are considered. Much insight into the solution of the regularized problem and into its limit for ε→ 0+ is obtained by the study of asymptotic expansions. Due to discontinuities in the derivative of the solution of the neutral delay equation and the presence of different time scales when crossing breaking points, new difficulties have to be managed. A new type of expansion (in powers of √ ε) turns out to be necessary for the study of the transition from weak to classical solutions. The techniques of this article can also be applied to the study of general singularly perturbed delay equations.

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عنوان ژورنال:
  • SIAM J. Math. Analysis

دوره 44  شماره 

صفحات  -

تاریخ انتشار 2012