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arXiv · 2209.03926

Topologies of continuity for Carath\'eodory parabolic PDEs from a dynamical perspective

Iacopo P. Longo·Rafael Obaya·Ana M. Sanz
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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.

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Iacopo P. Longo, Rafael Obaya, Ana M. Sanz. 2022-09-08. Topologies of continuity for Carath\'eodory parabolic PDEs from a dynamical perspective. https://arxiv.org/abs/2209.03926

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