2008/03/03 by Joachim Escher, Zhaoyang Yin · 67 citations
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Algebraic structures and combinatorial models #Boundary (topology) #Boundary value problem #Camassa–Holm equation #Cauchy boundary condition #Combinatorics #Free boundary problem #Geometry #Initial value problem #Integrable system #Interval (graph theory) #Mathematical analysis #Mathematics #Nonlinear Waves and Solitons #Symmetry (geometry)
paper · doi:10.1080/03605300701318872
published in Communications in Partial Differential Equations 33(3), 377-395 (Taylor & Francis)
openalex publication_date 2008/03/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
In this paper we study initial boundary value problems of the Camassa–Holm equation on the half line and on a compact interval. Using rigorously the conservation of symmetry, it is possible to convert these boundary value problems into Cauchy problems for the Camassa–Holm equation on the line and on the circle, respectively. Applying thus known results for the latter equations we first obtain the local well-posedness of the initial boundary value problems under consideration. Then we present some blow-up and global existence results for strong solutions. Finally we investigate global and local weak solutions for the equation on the half line and on a compact interval, respectively. An interesting result of our analysis shows that the Camassa–Holm equation on a compact interval possesses no nontrivial global classical solutions.