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Archive for Rational Mechanics and Analysis

, Volume 183, Issue 2, pp 215–239 | Cite as

Global Conservative Solutions of the Camassa–Holm Equation

  • Alberto Bressan
  • Adrian Constantin
Article

Abstract

This paper develops a new approach in the analysis of the Camassa–Holm equation. By introducing a new set of independent and dependent variables, the equation is transformed into a semilinear system, whose solutions are obtained as fixed points of a contractive transformation. These new variables resolve all singularities due to possible wave breaking. Returning to the original variables, we obtain a semigroup of global solutions, depending continuously on the initial data. Our solutions are conservative, in the sense that the total energy equals a constant, for almost every time.

Keywords

Initial Data Cauchy Problem Solitary Wave Global Solution Wave Breaking 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Department of MathematicsPennsylvania State UniversityUniversity ParkU.S.A.
  2. 2.School of MathematicsTrinity College DublinDublin 2Ireland
  3. 3.Department of MathematicsLund UniversityLundSweden

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