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Zbl 1190.35060
Lai, Shaoyong; Wu, Yonghong
Existence of weak solutions in lower order Sobolev space for a Camassa-Holm-type equation. (English)
[J] J. Phys. A, Math. Theor. 43, No. 9, Article ID 095205 (2010). ISSN 1751-8113; ISSN 1751-8121/e

Summary: A generalized Camassa-Holm equation containing a nonlinear dissipative effect is investigated. The existence of the weak solution of the equation in lower order Sobolev space $H^{s}$ with $1 < s \leqslant \frac{3}{2}$ is established by using the techniques of the pseudoparabolic regularization and some a priori estimates derived from the equation itself.

MSC 2000:: *35G25 Initial value problems for nonlinear higher-order PDE
35Q35 Other equations arising in fluid mechanics
35B45 A priori estimates
35D30

Keywords: nonlinear dissipative effect; pseudoparabolic regularization

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