OPTIMAL TRANSPORTATION METRICS AND NONLINEAR WAVE EQUATIONS

来源 :2006 International Conference on Analysis and Applications(I | 被引量 : 0次 | 上传用户:hgs061268109
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  The Camassa-Holm equation provides an example of a PDE generating a semigroup which is not Lipschitz continuous (or even continuous) w.r.t.any natural Banach norm.We will show that, for initial data in H1, a Gronwall-type estimate can be proved by introducing a suitable metric, defined in terms of a problem of optimal transportation.This yields the uniqueness and continuous dependence of conservative solutions.
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