2024/02/29 by Charles Bertucci, Pierre Louis Lions, Bertucci, Charles +1 · 1 citation
Mathematics · #Mathematical and Theoretical Analysis
paper · pdf · doi:10.48550/arxiv.2402.19092
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 x = f(x,x) for a function f: V× E → E where E is a Banach space and V \hookrightarrow 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.