共查询到20条相似文献,搜索用时 31 毫秒
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We consider the mixed initial–boundary value problem for the Benjamin–Ono equation on a half-line. We study traditionally important problems of the theory of nonlinear partial differential equations, such as global in time existence of solutions to the initial–boundary value problem and the asymptotic behavior of solutions for large time. 相似文献
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We consider the inhomogeneous Neumann initial–boundary value problem for the nonlinear Schrödinger equation, formulated on a half-line. We study traditionally important problems of the theory of nonlinear partial differential equations, such as global in time existence of solutions to the initial–boundary value problem and the asymptotic behavior of solutions for large time. 相似文献
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We prove global well-posedness results for small initial data in , and in , sk=1/2?1/k, for the generalized Benjamin–Ono equation . We also consider the cases k=2,3. To cite this article: L. Molinet, F. Ribaud, C. R. Acad. Sci. Paris, Ser. I 337 (2003). 相似文献
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G. I. Shishkin 《Computational Mathematics and Mathematical Physics》2017,57(11):1789-1795
An initial–boundary value problem for a singularly perturbed transport equation with a perturbation parameter ε multiplying the spatial derivative is considered on the set ? = G ∪ S, where ? = D? × [0 ≤ t ≤ T], D? = {0 ≤ x ≤ d}, S = S l ∪ S, and S l and S0 are the lateral and lower boundaries. The parameter ε takes arbitrary values from the half-open interval (0,1]. In contrast to the well-known problem for the regular transport equation, for small values of ε, this problem involves a boundary layer of width O(ε) appearing in the neighborhood of S l ; in the layer, the solution of the problem varies by a finite value. For this singularly perturbed problem, the solution of a standard difference scheme on a uniform grid does not converge ε-uniformly in the maximum norm. Convergence occurs only if h=dN-1 ? ε and N0-1 ? 1, where N and N0 are the numbers of grid intervals in x and t, respectively, and h is the mesh size in x. The solution of the considered problem is decomposed into the sum of regular and singular components. With the behavior of the singular component taken into account, a special difference scheme is constructed on a Shishkin mesh, i.e., on a mesh that is piecewise uniform in x and uniform in t. On such a grid, a monotone difference scheme for the initial–boundary value problem for the singularly perturbed transport equation converges ε-uniformly in the maximum norm at an ?(N?1 + N0?1) rate. 相似文献
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We prove existence and uniqueness of solutions for the Benjamin–Ono equation with data in \(H^{s}({\mathbb{R}})\) , s > 1/4. Moreover, the flow is hölder continuous in weaker topologies. 相似文献
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ZHANG Shuqin Department of Mathematics China University of Mining Technology Beijing 《中国科学A辑(英文版)》2006,49(9):1223-1230
Using the method of upper and lower solutions and its associated monotone iterative, consider the existence and uniqueness of solution of an initial value problem for the nonlinear fractional diffusion equation. 相似文献
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Nakao Hayashi Pavel I. Naumkin 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2008,59(6):1002-1028
We study the initial value problem for the cubic nonlinear Klein–Gordon equation
where μ ∈ R and the initial data are real-valued functions. We obtain a sharp asymptotic behavior of small solutions without the condition
of a compact support on the initial data which was assumed in the previous works.
相似文献
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Martin Kohlmann 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2012,63(3):441-452
The Hunter?CSaxton equation serves as a mathematical model for orientation waves in a nematic liquid crystal. The present paper discusses a modified variant of this equation, coming up in the study of critical points for the speed of orientation waves, as well as a two-component extension. We establish well-posedness and blow-up results for some initial boundary value problems for the modified Hunter?CSaxton equation and the two-component Hunter?CSaxton system. 相似文献
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This paper considers the IBVP of the Rosenau equation It is proved that this IBVP has a unique global distributional solution as initial data with . This is a new global well-posedness result on IBVP of the Rosenau equation with Dirichlet boundary conditions. 相似文献
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E. S. Baranovskii 《Computational Mathematics and Mathematical Physics》2016,56(7):1363-1371
The initial–boundary value problem for equations of motion of Kelvin–Voigt fluids with mixed boundary conditions is studied. The no-slip condition is used on some portion of the boundary, while the impermeability condition and the tangential component of the surface force field are specified on the rest of the boundary. The global-in-time existence of a weak solution is proved. It is shown that the solution is unique and depends continuously on the field of external forces, the field of surface forces, and initial data. 相似文献
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We prove that the periodic modified Benjamin–Ono equation is locally well-posed in the energy space H1/2. This ensures the global well-posedness in the defocusing case. The proof is based on an Xs,b analysis of the system after a gauge transform. 相似文献
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In this work we continue our study initiated in Fonseca and Ponce (2011) [11] on the uniqueness properties of real solutions to the IVP associated to the Benjamin–Ono (BO) equation. In particular, we shall show that the uniqueness results established in Fonseca and Ponce (2011) [11] do not extend to any pair of non-vanishing solutions of the BO equation. Also, we shall prove that the uniqueness result established in Fonseca and Ponce (2011) [11] under a hypothesis involving information of the solution at three different times cannot be relaxed to two different times. 相似文献
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In this paper we are concerned about a singular boundary value problem for a quasilinear second-order ordinary differential equation, involving the one-dimensional p-laplacian. Asymptotic expansions of the one-parameter families of solutions, satisfying the prescribed boundary conditions, are obtained in the neighborhood of the singular points and this enables us to compute numerical solutions using stable shooting methods. 相似文献
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Germán Fonseca Felipe Linares Gustavo Ponce 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2013
We study the initial value problem associated to the dispersion generalized Benjamin–Ono equation. Our aim is to establish persistence properties of the solution flow in weighted Sobolev spaces and to deduce from them some sharp unique continuation properties of solutions to this equation. In particular, we shall establish optimal decay rate for the solutions of this model. 相似文献