Journal of Integral Equations and Applications

Global existence and blow-Ups for certain ordinary integro-differential equations

Martin Saal

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We will study ordinary integro-differential equations of second order with nonlinearity given as a convolution, but differently from the widely investigated cases. In addition, the kernel depends on the solution. Such equations play a key role in the theory of glass-forming liquids, and we will establish results on global existence and investigate the long-term behavior. In contrast, we give examples where blow-ups occur.

Article information

J. Integral Equations Applications, Volume 27, Number 4 (2015), 573-602.

First available in Project Euclid: 8 February 2016

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Zentralblatt MATH identifier

Primary: 34A12: Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions 45G15: Systems of nonlinear integral equations 45J05: Integro-ordinary differential equations [See also 34K05, 34K30, 47G20]


Saal, Martin. Global existence and blow-Ups for certain ordinary integro-differential equations. J. Integral Equations Applications 27 (2015), no. 4, 573--602. doi:10.1216/JIE-2015-27-4-573.

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