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• W2949969894 abstract "The nonlinear wave equation $u_{tt}-c(u)(c(u)u_x)_x=0$ determines a flow of conservative solutions taking values in the space $H^1(mathbb{R})$. However, this flow is not continuous w.r.t. the natural $H^1$ distance. Aim of this paper is to construct a new metric which renders the flow uniformly Lipschitz continuous on bounded subsets of $H^1(mathbb{R})$. For this purpose, $H^1$ is given the structure of a Finsler manifold, where the norm of tangent vectors is defined in terms of an optimal transportation problem. For paths of piecewise smooth solutions, one can carefully estimate how the weighted length grows in time. By the generic regularity result proved in [7], these piecewise regular paths are dense and can be used to construct a geodesic distance with the desired Lipschitz property." @default.
• W2949969894 created "2019-06-27" @default.
• W2949969894 creator A5048359772 @default.
• W2949969894 creator A5084959058 @default.
• W2949969894 date "2015-06-20" @default.
• W2949969894 modified "2023-10-16" @default.
• W2949969894 title "Lipschitz Metrics for a Class of Nonlinear Wave Equations" @default.
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• W2949969894 doi "https://doi.org/10.48550/arxiv.1506.06310" @default.
• W2949969894 hasPublicationYear "2015" @default.
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