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.

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-11 and codimension-22 weak solutions are considered. Numerical experiments show the advantages of the new regularization.

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

GUGLIELMI, NICOLA;
2016-01-01

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.
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-11 and codimension-22 weak solutions are considered. Numerical experiments show the advantages of the new regularization.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11697/108397
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