Well-posedness of Linear Integro-Differential Equations with Operator-valued Kernels
Analysis of PDEs
2016-04-05 v3 Functional Analysis
Abstract
We study linear integro-differential equations in Hilbert spaces with operator-valued kernels and give sufficient conditions for the well-posedness. We show that several types of integro-differential equations are covered by the class of evolutionary equations introduced in [R. Picard. A structural observation for linear material laws in classical mathematical physics. Math. Methods Appl. Sci., 32(14):1768-1803, 2009]. We therefore give criteria for the well-posedness within this framework. As an example we apply our results to the equations of visco-elasticity.
Cite
@article{arxiv.1210.1728,
title = {Well-posedness of Linear Integro-Differential Equations with Operator-valued Kernels},
author = {Sascha Trostorff},
journal= {arXiv preprint arXiv:1210.1728},
year = {2016}
}
Comments
For a revised version of the article see "On Integro-Differential Inclusions with Operator-valued Kernels" arXiv:1308.4782