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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