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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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