On ill-posedness for the generalized BBM equation
نویسندگان
چکیده
منابع مشابه
On the Ill-posedness Result for the Bbm Equation
We prove that the initial value problem (IVP) for the BBM equation is ill-posed for data in H(R), s < 0 in the sense that the flow-map u0 7→ u(t) that associates to initial data u0 the solution u cannot be continuous at the origin from H(R) to even D′(R) at any fixed t > 0 small enough. This result is sharp.
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An approach is proposed to obtain some exact explicit solutions in terms of the Weierstrass’ elliptic function ℘ to a generalized Benjamin-Bona-Mahony (BBM) equation. Conditions for periodic and solitary wave like solutions can be expressed compactly in terms of the invariants of ℘. The approach unifies recently established ad-hoc methods to a certain extent. Evaluation of a balancing principle...
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The concern of this paper is the Cauchy problem for the Prandtl equation. This problem is known to be well-posed for analytic data [13, 10], or for data with monotonicity properties [11, 15]. We prove here that it is linearly ill-posed in Sobolev type spaces. The key of the analysis is the construction, at high tangential frequencies, of unstable quasimodes for the linearization around solution...
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ژورنال
عنوان ژورنال: Discrete and Continuous Dynamical Systems
سال: 2014
ISSN: 1078-0947
DOI: 10.3934/dcds.2014.34.4565