We prove a reducibility result for linear wave equation with time quasi-periodic driving on the one dimensional torus. The is assumed to be fast oscillating, but not necessarily of small size. Provided that external frequency vector sufficiently large and chosen from Cantor set measure, original conjugated time-independent, block-diagonal one. With present paper, we extend previous work [26] mo...

In this paper, we study the Cauchy problem for Benjamin-Ono-Burgers equation $${\partial _t}u - \epsilon \partial _x^2u + {\cal H}\partial u{u_x} = 0$$ , where $${\cal H}$$ denotes Hilbert transform operator. We obtain that it is uniformly locally well-posed small data in refined Sobolev space $${\tilde H^\sigma }(\mathbb{R})\,\,(\sigma \geqslant 0)$$ which a subspace of L2(ℝ). It worth noting ...

In this paper, we represent an inexact inverse subspace iteration method for computing a few eigenpairs of the generalized eigenvalue problem Ax = Bx [Q. Ye and P. Zhang, Inexact inverse subspace iteration for generalized eigenvalue problems, Linear Algebra and its Application, 434 (2011) 1697-1715 ]. In particular, the linear convergence property of the inverse subspace iteration is preserved.

In this paper we prove compact embedding of a subspace the fractional Orlicz-Sobolev space $W^{s, G}\left(\mathbb{R}^{N}\right)$ consisting radial functions, our target spaces are Orlicz type. Also, Lions and Lieb type results for $W^{s,G}\left(\mathbb{R}^{N}\right)$ that works together in particular way to get sequence whose weak limit is nontrivial. As an application, study existence solution...

Image modeling stays at the very core of image processing and low-level vision analysis. In the Bayesian framework, image modeling amounts to the introduction of suitable prior models, while in the Tikhonov framework [47], to the specification of regularity structures in order to better condition ill-posed inverse tasks such as denoising or deblurring. In the variational approach [3, 10, 40, 41...

Let L := −r−2(r∂r )2 − ∂2 z . We consider the equation Lu = f on a bounded polygonal domain with suitable boundary conditions, derived from the three-dimensional axisymmetric Poisson’s equation. We establish the well-posedness, regularity, and Fredholm results in weighted Sobolev spaces, for possible singular solutions caused by the singular coefficient of the operator L, as r → 0, and by non-s...

Let L := −r−2(r∂r)2 − ∂2 z . We consider the equation Lu = f on a bounded polygonal domain with suitable boundary conditions, derived from the three-dimensional axisymmetric Poisson’s equation. We establish the well-posedness, regularity and Fredholm results in weighted Sobolev spaces, for possible singular solutions caused by the singular coefficient of the operator L, as r → 0, and by non-smo...

In Hilbert space L2(Rn), we prove the equivalence between the mod-ulus of smoothness and the K-functionals constructed by the Sobolev space cor-responding to the Fourier transform. For this purpose, Using a spherical meanoperator.