Dissipative Hyperbolic Geometric Flow

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In this paper we introduce and study a new kind of hyperbolic geometric flows --dissipative hyperbolic geometric flow. This kind of flow is defined by a system of quasilinear wave equations with dissipative terms. Some interesting exact solutions are given, in particular, a new concept-- hyperbolic Ricci soliton is introduced and some of its geometric properties are described. We also establish the short-time existence and uniqueness theorem for the dissipative hyperbolic geometric flow, and prove the nonlinear stability of the flow defined on the Euclidean space of dimension larger than 2. Wave character of the evolving metrics and curvatures is illustrated and the nonlinear wave equations satisfied by the curvatures are derived.

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Differential Geometry, Analysis of PDEs

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http://salesiana.dossiersoluciones.com/handle/123456789/138124

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0709.2542
 http://arxiv.org/abs/0709.2542

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arXiv