The local strong and weak solutions to a generalized Novikov equation
Department of Mathematics, Southwestern University of Finance and Economics, Chengdu, 610074, China
Boundary Value Problems 2013, 2013:134 doi:10.1186/1687-2770-2013-134Published: 20 May 2013
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 is established under the assumptions and .
MSC: 35Q35, 35Q51.