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The existence of global weak solutions of the Cauchy problem for a generalized Dullin-Gottwald-Holm equation is established under the assumption that the initial value u 0 ( x ) $u_{0}(x)$ merely lies in the space H 1 ( R ) $H^{1}(R)$ . The limit of the viscous approximation for the equation is used to prove the global existence in the space C ( [ 0 , ∞ ) × R ) ∩ L ∞ (...
A nonlinear partial differential equation, which includes the Novikov equation as a special case, is investigated. The well-posedness of local strong solutions for the equation in the Sobolev space with is established. Although the -norm of the solutions to the nonlinear model does not remain constant, the existence of its local weak solutions in the lower order Sobolev space with...
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