共查询到20条相似文献,搜索用时 15 毫秒
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Mauro Antonio Rincon Maria Inês Martins Copetti 《Journal of Applied Analysis & Computation》2013,3(2):169-182
We consider a semi-discrete finite element formulation with artificial viscosity for the numerical approximation of a problem that models the damped vibrations of a string with fixed ends. The damping coefficient depends on the spatial variable and is effective only in a sub-interval of the domain. For this scheme, the energy of semi-discrete solutions decays exponentially and uniformly with respect to the mesh parameter to zero. We also introduce an implicit in time discretization. Error estimates for the semi-discrete and fully discrete schemes in the energy norm are provided and numerical experiments performed. 相似文献
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Rafael Carreño-Bolaños Beatriz Juarez-Campos Pavel I. Naumkin 《Studies in Applied Mathematics》2020,145(1):137-149
We study the nonlinear damped wave equation with a linear pumping and a convective nonlinearity. We consider the solutions, which satisfy the periodic boundary conditions. Our aim is to prove global existence of solutions to the periodic problem for the nonlinear damped wave equation by applying the energy-type estimates and estimates for the Green operator. Moreover, we study the asymptotic profile of global solutions. 相似文献
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Takashi Narazaki 《Journal of Mathematical Analysis and Applications》2008,338(2):803-819
We consider the Cauchy problem for the damped wave equation
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We consider a viscoelastic wave equation with power nonlinearity. First, we construct a local solution by the Faedo-Galerkin approximation scheme and contraction mapping theorem. Next, we continue the local solution to the global one by a priori estimates obtained from a decreasing energy. Finally, we discuss the decay rate of the global solution by assuming that the kernel function is convex. 相似文献
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Isabella Fabbri 《Journal of Mathematical Analysis and Applications》2010,369(1):179-187
Given Ω a smooth bounded domain of Rn, n?3, we consider functions that are weak solutions to the equation
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We consider the Cauchy problem for the third‐order nonlinear Schrödinger equation where and is the Fourier transform. Our purpose in this paper is to prove the large time asymptoitic behavior of solutions for the defocusing case λ > 0 with a logarithmic correction under the non zero mass condition Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
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S. V. Zelik 《Mathematical Notes》1997,61(4):451-464
The behavior ast→∞ of solutions of the equation
in a Hilbert space is studied, whereA=A
* is a positive definite operator with compact inverse and the operatorf is periodic int. The notion of instability index is introduced for this equation; we prove that the instability index is finite under natural
assumptions (f must be dominated byA). Asymptotic estimates of the instability index are obtained as γ→0, and an example is constructed showing that they cannot
be improved. Furthermore, we study the qualitative characteristics of the spectrum of the monodromy operator and the existence
of the Floquet representation for this problem.
Translated fromMatematicheskie Zametki, Vol. 61, No. 4, pp. 543–560, April, 1997.
Translated by A. M. Chebotarev 相似文献
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Martin Ondreját 《Journal of Differential Equations》2010,248(7):1579-1602
We consider a nonlinear wave equation on Rd driven by a spatially homogeneous Wiener process W with a finite spectral measure and with nonlinear terms f, g of critical growth. We study pathwise uniqueness and norm continuity of paths of (u,ut) in H1(Rd)⊕L2(Rd) under the hypothesis that there exists a local solution u such that (u,ut) has weakly continuous paths in H1(Rd)⊕L2(Rd). 相似文献
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J. Berkovits 《Journal of Mathematical Analysis and Applications》2007,332(1):691-699
We shall prove a weakened Ambrosetti-Prodi type multiplicity result for a wave equation with sublinear nonlinearity and without damping. Due to infinite-dimensional kernel of the wave operator, the Leray-Schauder and coincidence degrees are not available. We use an extension of the Leray-Schauder degree to obtain multiple solutions. 相似文献
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In this paper, we investigate the Cauchy problem of the nonlinear wave equation , where V(u) = μ|·|?γ ? |u|2, , 0 < γ < min(4, n) and n ≥ 3. We prove small data global well‐posedness for the radial data and for the general data with angular regularity. We also give an improved result of the Hartree equation with negative critical regularity. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
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P. Freitas 《Journal of Differential Equations》2005,211(1):168-186
We extend some previous results for the damped wave equation in bounded domains in to the unbounded case. In particular, we show that if the damping term is of the form αa with bounded a taking on negative values on a set of positive measure, then there will always exist unbounded solutions for sufficiently large positive α.In order to prove these results, we generalize some existing results on the asymptotic behaviour of eigencurves of one-parameter families of Schrödinger operators to the unbounded case, which we believe to be of interest in their own right. 相似文献