On the Cauchy problem for higher-order nonlinear dispersive equations
نویسندگان
چکیده
منابع مشابه
On the Cauchy problem for higher-order nonlinear dispersive equations
We study the higher-order nonlinear dispersive equation ∂tu+ ∂ 2j+1 x u = ∑ 0≤j1+j2≤2j aj1,j2∂ j1 x u∂ j2 x u, x, t ∈ R. where u is a real(or complex-) valued function. We show that the associated initial value problem is well posed in weighted Besov and Sobolev spaces for small initial data. We also prove ill-posedness results when a0,k 6= 0 for some k > j, in the sense that this equation cann...
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iut + Lu = F (u), (1) where u : IR × IR → I C and L is a linear (pseudo -) differential operator of order m with real valued symbol denoted by l(ξ), and F is a nonlinear, possibly nonlocal operator. We will only consider the case where the linear part of (1) is dispersive, i.e. l(ξ) 6= Cξ. Actually, we will address cases where the linear group e satisfies some “decay” properties, see Section 1....
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ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 2008
ISSN: 0022-0396
DOI: 10.1016/j.jde.2008.07.017