The Local Strong and Weak Solutions for a Nonlinear Dissipative Camassa-Holm Equation | Zendy

Shaoyong Lai | Zendy

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The Local Strong and Weak Solutions for a Nonlinear Dissipative Camassa-Holm Equation

Author(s) -

Shaoyong Lai

Publication year - 2011

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2011/285040

Subject(s) - mathematics , dissipative system , camassa–holm equation , sobolev space , nonlinear system , mathematical analysis , space (punctuation) , order (exchange) , weak solution , mathematical physics , physics , thermodynamics , integrable system , quantum mechanics , linguistics , philosophy , finance , economics

Using the Kato theorem for abstract differential equations, the local well-posedness of the solution for a nonlinear dissipative Camassa-Holm equation is established in space C([0,T),Hs(R))∩C1([0,T),Hs-1(R)) with s>3/2. In addition, a sufficient condition for the existence of weak solutions of the equation in lower order Sobolev space Hs(R) with 1≤s≤3/2 is developed

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