Topologies of continuity for Carath\'eodory parabolic PDEs from a dynamical perspective
Dynamical Systems
2022-09-09 v1
Abstract
Systems of non-autonomous parabolic partial differential equations over a bounded domain with nonlinear term of Carath\'eodory type are considered. Appropriate topologies on sets of Lipschitz Carath\'eodory maps are defined in order to have a continuous dependence of the mild solutions with respect to the variation of both the nonlinear term and the initial conditions, under different assumptions on the bound-maps of the nonlinearities.
Keywords
Cite
@article{arxiv.2209.03926,
title = {Topologies of continuity for Carath\'eodory parabolic PDEs from a dynamical perspective},
author = {Iacopo P. Longo and Rafael Obaya and Ana M. Sanz},
journal= {arXiv preprint arXiv:2209.03926},
year = {2022}
}
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28 pgs