Projects

We consider various initial-value problems for partial integro-differential equations of first order that are characterized by convolution-terms in the time-variable, where all factors depend on the solutions of the equations. The mathematical structure of such problems is based on problems for ordinary integro-differential equations that are used to describe certain glass-transition phenomena. We start considering problems with kernels that are not depending on the space-variable and we will prove results concerning well-posedness and asymptotic behaviour. Afterwards, we will extend the results on problems with kernels that depend on the space-variable.

We consider various initial-value problems for ordinary integro-differential equations of first order that are characterized by convolution-terms, where all factors depend on the solutions of the equations. Applications of such problems are descriptions of certain glass-transition phenomena based on mode-coupling theory, for instance. We will prove results concerning well-posedness of such problems and the asymptotic behaviour of their solutions.