Nicola Guglielmi
Institute
L'Aquila
Address
Presentation
oral
(Plenary talk)
Title
Talk 1: On singular perturbations of delay differential equations.
Title 2: A regularization for discontinuous differential equations.
Abstract
Talk 1.
In the context of the regularization of delay
differential equations with state dependent delays it is natural to introduce singular perturbations.
In the talk I will consider two classes of singularly perturbed delay differential equations and discuss the properties of their solutions. In particular I shall analyze the convergence of the solutions when the parameter associated to the singular perturbation vanishes.
In this way one can hope to define a weak solution of the problem and also to determine a modified system of differential equations for such weak solution.
Finally I shall discuss the numerical integration
explaining some peculiar aspects concerned with both the approaches.
This is a joint work with Giorgio Fusco and Ernst Hairer.
Talk (CT) 2. I will introduce a regularization for discontinuous differential equations based on an average in time of the vectorfield.
I will first discuss local existence of the solution of the regularized problem and then examine the behaviour of the solution as the regularization parameter tends to zero.
Some examples will illustrate the main features
of the considered regularization.
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