On well-posedness for some Korteweg-De Vries type equations with variable coefficients
Luc Molinet,
Raafat Talhouk,
Ibtissame Zaiter
Abstract:In this paper, KdV-type equations with time-and space-dependent coefficients are considered. Assuming that the dispersion coefficient in front of uxxx is positive and uniformly bounded away from the origin and that a primitive function of the ratio between the anti-dissipation and the dispersion coefficients is bounded from below, we prove the existence and uniqueness of a solution u such that hu belongs to a classical Sobolev space, where h is a function related to this ratio. The LWP in H s (R), s > 1/2, in … Show more
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