For neutral delay differential equations the right-hand side can be multi-valued, when one or several delayed arguments cross a breaking point. This article studies a regularization via a singularly perturbed problem, which smooths the vector field and removes the discontinuities in the derivative of the solution. A low-dimensional dynamical system is presented, which characterizes the kind of generalized solution that is approximated. For the case that the solution of the regularized problem has high frequency oscillations around a codimension-2 weak solution of the original problem, a new stabilizing regularization is proposed and analyzed.

### Regularization of neutral delay differential equations with several delays

#### Abstract

For neutral delay differential equations the right-hand side can be multi-valued, when one or several delayed arguments cross a breaking point. This article studies a regularization via a singularly perturbed problem, which smooths the vector field and removes the discontinuities in the derivative of the solution. A low-dimensional dynamical system is presented, which characterizes the kind of generalized solution that is approximated. For the case that the solution of the regularized problem has high frequency oscillations around a codimension-2 weak solution of the original problem, a new stabilizing regularization is proposed and analyzed.
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2013
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11697/16488`
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