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Path-regularization of linear neutral delay differential equations with several delays

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N. Guglielmi and E. Hairer

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Abstract. For differential equations with discontinuous right-hand side and, in particular, for neutral delay equations it may happen that classical solutions do no exist beyond a certain time instant. In this situation, it is common to consider weak solutions of Utkin (Filippov) type. This article extends the concept of weak solutions and proposes a new regularization which eliminates the discontinuities. Codimension-1 and codimension-2 weak solutions are considered. Numerical experiments show the advantages of the new regularization.

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Key Words. Neutral delay equations, weak solutions, discontinuous differential equations, path-regularization, stability.

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