نتایج جستجو برای: posed problem

تعداد نتایج: 897445  

2007
Dang Duc Trong Nguyen Thanh Long Pham Ngoc Dinh

We study the nonhogeneous heat equation under the form: u t ? u xx = '(t)f(x), where the unknown is the pair of functions (u; f). Under various assumptions about the the function ' and the nal value in t = 1 i.e. g(x), we propose diierent regularizations on this ill-posed problem based on the Fourier transform associated with a Lebesgue measure. For ' 6 6 0 the solution is unique. I. Introducti...

2017
Junfang Wang Zongmin Wang

Here u(x, t) represents the free surface of the liquid and the parameter γ > 0 measures the effect of rotation. (1.1) describes the propagation of internal waves of even modes in the ocean; for instance, see the work of Galkin and Stepanyants [1], Leonov [2], and Shrira [3, 4]. The parameter β determines the type of dispersion, more precisely, when β < 0, (1.1) denotes the generalized Ostrovsky...

Journal: :Appl. Math. Lett. 2006
C. L. Farmer Sam D. Howison

We consider the motion of a thin filament of viscous fluid in a HeleShaw cell. The appropriate thin film analysis and use of Lagrangian variables leads to the Cauchy-Riemann system in a surprisingly direct way. We illustrate the inherent ill-posedness of these equations in various contexts.

2009
PENGTAO LI ZHICHUN ZHAI

In this paper, we prove the boundedness of Riesz transforms ∂j(−∆) (j = 1, 2, · · · , n) on the Q-type spaces Qα(R n). As an application, we get the well-posedness and regularity of the quasi-geostrophic equation with initial data in Q α (R ).

2008
Junfeng Li Jie Xiao

In this paper we establish the local and global well-posedness of the real valued fifth order Kadomstev-Petviashvili I equation in the anisotropic Sobolev spaces with nonnegative indices. In particular, our local well-posedness improves SautTzvetkov’s one and our global well-posedness gives an affirmative answer to SautTzvetkov’s L-data conjecture.

2008
Jun Kato Herbert Koch

We establish the local well-posedness of the modified Schrödinger map in H3/4+ε(R2).

2012
Xinwei Yu Zhichun Zhai Congming Li ZHICHUN ZHAI

In this article we study local and global well-posedness of the Lagrangian Averaged Euler equations. We show local well-posedness in TriebelLizorkin spaces and further prove a Beale-Kato-Majda type necessary and sufficient condition for global existence involving the stream function. We also establish new sufficient conditions for global existence in terms of mixed Lebesgue norms of the general...

2016
Abdugeni Osman Abdukerim Haji A. Osman A. Haji

We investigate the solution of an N-unit series system with finite number of vacations. By using CC00-semigroup theory of linear operators, we prove well-posedness and the existence of the unique positive dynamic solution of the system.

2016
Hoai-Minh Nguyen

Article history: Received 31 August 2015 Available online 27 February 2016 MSC: 35B34 35B35 35B40 35J05 78A25

2010
TAKAMORI KATO

We consider the Cauchy problem for the KdV equation with low regularity initial data given in the space Hs,a(R), which is defined by the norm ‖φ‖Hs,a = ‖〈ξ〉s−a|ξ|a b φ‖L2 ξ . We obtain the local well-posedness in Hs,a with s ≥ max{−3/4,−a − 3/2}, −3/2 < a ≤ 0 and (s, a) 6= (−3/4,−3/4). The proof is based on Kishimoto’s work [12] which proved the sharp well-posedness in the Sobolev space H−3/4(R...

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