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On integro‐differential inclusions with operator‐valued kernels
Authors:
Sascha Trostorff
Institution:
Institut für Analysis, Fachrichtung Mathematik, Technische Universit?t Dresden, Germany
Abstract:
We study integro‐differential inclusions in Hilbert spaces with operator‐valued kernels and give sufficient conditions for the well‐posedness. We show that several types of integro‐differential equations and inclusions are covered by the class of evolutionary inclusions, and we therefore give criteria for the well‐posedness within this framework. As an example, we apply our results to the equations of visco‐elasticity and to a class of nonlinear integro‐differential inclusions describing phase transition phenomena in materials with memory. Copyright © 2014 John Wiley & Sons, Ltd.
Keywords:
integro‐differential inclusions and equations
well‐posedness and causality
evolutionary inclusions
linear material laws
maximal monotone operators
visco‐elasticity
phase transition models
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