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Nonlocal heat flows preserving the L2 energy

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  • We shall study L2 energy conserved solutions to the heat equation.We shall first establish the global existence, uniqueness andregularity of solutions to such nonlocal heat flows. We then extend themethod to a family of singularly perturbed systems of nonlocal parabolicequations. The main goal is to show that solutions to these perturbedsystems converges strongly to some suitable weak-solutionsof the limiting constrained nonlocal heat flows of maps into a singularspace. It is then possible to study further properties of such suitableweak solutions and the corresponding free boundary problem, which willbe discussed in a forthcoming article.
    Mathematics Subject Classification: Primary: 35K05, 35K55; Secondary: 49N60.


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