• Corpus ID: 201646354

# Weak solutions for gradient flows under monotonicity constraints

@article{Negri2019WeakSF,
title={Weak solutions for gradient flows under monotonicity constraints},
author={Matteo Negri and Masato Kimura},
journal={arXiv: Analysis of PDEs},
year={2019}
}
• Published 27 August 2019
• Mathematics
• arXiv: Analysis of PDEs
We consider the gradient flow of a quadratic non-autonomous energy under monotonicity constraint in time and natural regularity assumptions. We provide first a notion of weak solution, inspired by the theory of curves of maximal slope, and then existence (employing time-discrete schemes with different "implementations" of the constraint), uniqueness, power and energy identity, comparison principle and continuous dependence. As a byproduct, we show that the energy identity gives a selection…

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