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Pré-Publication, Document De Travail Année : 2024

A two spaces extension of Cauchy-Lipschitz Theorem

Résumé

We adapt the classical theory of local well-posedness of evolution problems to cases in which the nonlinearity can be accurately quantified by two different norms. For ordinary differential equations, we consider ẋ = f (x, x) for a function f : V × E → E where E is a Banach space and V → E a normed vector space. This structure allows us to distinguish between the two dependencies of f in x and allows to generalize classical results. We also prove a similar results for partial differential equations.
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Dates et versions

hal-04482225 , version 1 (28-02-2024)

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Charles Bertucci, Pierre Louis Lions. A two spaces extension of Cauchy-Lipschitz Theorem. 2024. ⟨hal-04482225⟩
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