# 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} }

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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