Analysis and Numerics of Evolution with Applications in the Science

Participants
Institutions
  • FB Physik
Publications
  Kurth, Patrick (2014): On a new class of Integro-Differential Equations (Konstanzer Schriften in Mathematik; 326)

On a new class of Integro-Differential Equations

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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.

Origin (projects)

  Kurth, Patrick (2014): On a new class of Partial Integro-Differential Equations (Konstanzer Schriften in Mathematik; 327)

On a new class of Partial Integro-Differential Equations

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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.

Origin (projects)

Funding sources
Name Project no. Description Period
Sonstige DFG792/09no information
Further information
Period: 01.04.2010 – 31.03.2012