共查询到20条相似文献,搜索用时 0 毫秒
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Chunqiu Li Cheng Hsiung Hsu Jian Jhong Lin 《Journal of Difference Equations and Applications》2013,19(10):1404-1426
The purpose of this work is to investigate the asymptotic behaviours of solutions for the discrete Klein–Gordon–Schrödinger type equations in one-dimensional lattice. We first establish the global existence and uniqueness of solutions for the corresponding Cauchy problem. According to the solution's estimate, it is shown that the semi-group generated by the solution is continuous and possesses an absorbing set. Using truncation technique, we show that there exists a global attractor for the semi-group. Finally, we extend the criteria of Zhou et al. [S. Zhou, C. Zhao, and Y. Wang, Finite dimensionality and upper semicontinuity of compact kernel sections of non-autonomous lattice systems, Discrete Contin. Dyn. Syst. A 21 (2008), pp. 1259–1277.] for finite fractal dimension of a family of compact subsets in a Hilbert space to obtain an upper bound of fractal dimension for the global attractor. 相似文献
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Jason Murphy 《偏微分方程通讯》2015,40(2):265-308
We study the defocusing nonlinear Schrödinger equation in three space dimensions. We prove that any radial solution that remains bounded in the critical Sobolev space must be global and scatter. In the energy-supercritical setting we employ a space-localized Lin–Strauss Morawetz inequality of Bourgain. In the intercritical regime we prove long-time Strichartz estimates and frequency-localized Lin–Strauss Morawetz inequalities. 相似文献
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We derive the long-time asymptotics for solutions of the discrete 1D Schrödinger and Klein–Gordon equations. 相似文献
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In this paper, we study the global well-posedness below the energy norm of the Cauchy problem for the Klein–Gordon system in R3. We prove the Hs-global well-posedness with s<1 of the Cauchy problem for the Klein–Gordon system. The method invoked is different from the well-known Bourgain’s method [Jean Bourgain, Refinements of Strichartz’s inequality and applications to 2D-NLS with critical nonlinearity, International Mathematial Research Notices 5 (1998) 253–283]. 相似文献
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In this paper, we propose an efficient numerical scheme for the space-fractional Klein–Gordon–Schrödinger (SFKGS) equations. Motivated by the “Invariant Energy Quadratization” (IEQ) approach, we introduce two auxiliary variables to transform the SFKGS system into a new equivalent system in which the time derivative is discretized by the Crank–Nicolson method, and the space discretization is based on the Fourier spectral method. Consequently, the numerical scheme shares two good features. The first feature is that the nonlinear terms are treated semi-explicitly and a linear symmetric system is solved at each time step. The second feature is the energy conservation at the discrete level. These two advantages are proved by the theoretical analysis and illustrated by a given numerical example. 相似文献
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Under study is the Cauchy problem for the fractional diffusion equation with a Caputo derivative. The existence and uniqueness theorems for a smooth solution are proven in a weighted H¨older space. 相似文献
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In this paper we study the Cauchy problem for cubic nonlinear Schrödinger equation with space- and time-dependent coefficients on ∝m and \(\mathbb{T}^m \). By an approximation argument we prove that for suitable initial values, the Cauchy problem admits unique local solutions. Global existence is discussed in the cases of m = 1, 2. 相似文献
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In this paper, we design a linear-compact conservative numerical scheme which preserves the original conservative properties to solve the Klein–Gordon–Schrödinger equation. The proposed scheme is based on using the finite difference method. The scheme is three-level and linear-implicit. Priori estimate and the convergence of the finite difference approximate solutions are discussed by the discrete energy method. Numerical results demonstrate that the present scheme is conservative, efficient and of high accuracy. 相似文献
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Sh. M. Nasibov 《Doklady Mathematics》2018,98(3):586-588
The solution of the Cauchy problem for a nonlinear Schrödinger evolution equation with certain initial data is proved to blow up in a finite time, which is estimated from above. Additionally, lower bounds for the blow-up rate are obtained in some norms. 相似文献
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Clément Gallo 《偏微分方程通讯》2013,38(5):729-771
For rather general nonlinearities, we prove that defocusing nonlinear Schrödinger equations in ? n (n ≤ 4), with non-vanishing initial data at infinity u 0, are globally well-posed in u 0 + H 1. The same result holds in an exterior domain in ? n , n = 2, 3. 相似文献
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《Journal of Computational and Applied Mathematics》1988,21(2):161-171
In this paper, we construct the conservative spectral scheme for the periodic initial-value problem for a system of equations of the complex Schrödinger field, interacting with the real Klein—Gordon field and estimate the error which is \xV;\GF;(nk) − ΦnN\xV; + \xV;χ(nk) − iXnn\xV;1 = O(k2 + N−(γ−1)). 相似文献
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Multiple solutions for nonhomogeneous Schrödinger–Maxwell and Klein– Gordon–Maxwell equations on R
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Shang-Jie Chen Chun-Lei Tang 《NoDEA : Nonlinear Differential Equations and Applications》2010,17(5):559-574
In this paper we study the following nonhomogeneous Schrödinger–Maxwell equations $\left\{\begin{array}{ll} {-\triangle u+V(x)u+ \phi u=f(x,u)+h(x),} \quad {\rm in}\,\,\,{\mathbf{R}}^3,\\ {-\triangle \phi=u^2, \qquad\qquad\qquad\qquad\qquad\qquad\,\,\, {\rm in} \,\,{\mathbf{R}}^3,} \end{array} \right.$ where f satisfies the Ambrosetti–Rabinowitz type condition. Under appropriate assumptions on V, f and h, the existence of multiple solutions is proved by using the Ekeland’s variational principle and the Mountain Pass Theorem in critical point theory. Similar results for the nonhomogeneous Klein–Gordon–Maxwell equations $\left\{\begin{array}{ll} {-\triangle u+[m^2-(\omega+\phi)^2]u=|u|^{q-2}u+h(x), \quad {\rm in} \,\,\,{\mathbf{R}}^3,}\\ {-\triangle \phi+ \phi u^2=-\omega u^2, \qquad\qquad\qquad\qquad\qquad\,\,\, {\rm in} \,\,\,{\mathbf{R}}^3,} \end{array} \right.$ are also obtained when 2 < q < 6. 相似文献
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In this work we study the asymptotic behavior of the solutions of the linear Klein–Gordon equation in RN, N?1. We prove that local energy of solutions to the Cauchy problem decays polynomially. Afterwards, we use the local decay of energy to study exact boundary controllability for the linear Klein–Gordon equation in general bounded domains of RN, N?1. 相似文献