On a new class of Partial Integro-Differential Equations

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2014
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Analysis and Numerics of Evolution with Applications in the Science
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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.

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510 Mathematik
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integro-differential equations, well-posedness, asymptotic behaviour, convolution
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ISO 690KURTH, Patrick, 2014. On a new class of Partial Integro-Differential Equations
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@techreport{Kurth2014class-26539,
  year={2014},
  series={Konstanzer Schriften in Mathematik},
  title={On a new class of Partial Integro-Differential Equations},
  number={327},
  author={Kurth, Patrick}
}
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