查看更多>>摘要：In this paper, we study the indirect stabilization of a coupled string-beam system related to the well-known Lazer-McKenna suspension bridge model. We prove some decay results of the energy of the system with either interior dampings or boundary ones. Our method is based on observ-ability estimates of the undamped system and on the spectral analysis of the spatial operator.
查看更多>>摘要：We consider a quasi-linear homogenization problem in a two-dimensional pre-fractal domain Omega(n), for n is an element of N, surrounded by thick fibers of amplitude epsilon. We introduce a sequence of "pre-homogenized" energy functionals, and we prove that this sequence converges in a suitable sense to a quasi-linear fractal energy functional involving a p-energy on the fractal boundary. We prove existence and uniqueness results for (quasi-linear) pre-homogenized and homogenized fractal problems. The convergence of the solutions is also investigated.
Kirilov, Alexandrede Moraes, Wagner A. A.Ruzhansky, Michael
27页
查看更多>>摘要：In this paper, we characterize completely the global hypoellipticity and global solvability in the sense of Komatsu (of Roumieu and Beurling types) of constant-coefficient vector fields on compact Lie groups. We also analyze the influence of perturbations by lower-order terms in the preservation of these properties.
查看更多>>摘要：We consider the Cauchy problem for the inhomogeneous nonlinear Schrodinger (INLS) equation iu(t) + Delta u = vertical bar x vertical bar(-b)f (u), u(0) = u(0) is an element of H-s(R-n), where 0 < s < min{n, n/2 + 1}, 0 < b min{2, n - s, 1 + n-2s/2} and f (u) is a nonlinear function 2 that behaves like lambda vertical bar u vertical bar(sigma) u with lambda is an element of C and sigma > 0, We prove that the Cauchy problem of the INLS equation is globally well-posed in H-s(R-n) if the initial data is sufficiently small and sigma(0) < sigma < sigma(s), where sigma(0) = 4-2b/n and sigma(s) = 4-2b/n-2s if s < n/2, sigma(s) = infinity if s >= n/2. Our global well-posedness result improves the one of Guzman [Nonlinear Anal. Real World Appl. 37 (2017), 249-286] by extending the validity of s and b. In addition, we also have the small data scattering result.
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