We consider a generalization of the Boussinesq equation obtained by adding a term of the form a(t, x, u)∂3xu. We prove local in time well-posedness of the Cauchy problem in Sobolev spaces under a suitable decay condition on the real part of the coefficient a(t, x, u), as x → ∞.
CITATION STYLE
Ascanelli, A., & Boiti, C. (2015). Well-posedness for a generalized boussinesq equation. In Trends in Mathematics (Vol. 2, pp. 193–202). Springer International Publishing. https://doi.org/10.1007/978-3-319-12577-0_23
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