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141.
We study the eigenvalue problem for the Dirichlet Laplacian in bounded simply connected plane domains by reducing it, using conformal transformations, to the weighted eigenvalue problem for the Dirichlet Laplacian in the unit disc . This allows us to estimate the variation of the eigenvalues of the Dirichlet Laplacian upon domain perturbation via energy type integrals for a large class of “conformal regular” domains which includes all quasidiscs, i.e. images of the unit disc under quasiconformal homeomorphisms of the plane onto itself. Boundaries of such domains can have any Hausdorff dimension between one and two. 相似文献
142.
We consider the study of an eigenvalue problem obtained by linearizing about solitary wave solutions of a Boussinesq equation. Instead of using the technique of Evans functions as done by Pego and Weinstein in [R. Pego and M. Weinstein, Convective Linear Stability of Solitary Waves for Boussinesq equation. AMS, 99, 311–375] for this particular problem, we perform Fourier analysis to characterize solutions of the eigenvalue problem in terms of a multiplier operator and use the strong relationship between the eigenvalue problem for the linearized Boussinesq equation and the eigenvalue problem associated with the linearization about solitary wave solutions of a special form of the KdV equation. By using a generalization of the Rouché Theorem and the asymptotic behavior of the Fourier symbol corresponding to the eigenvalues problem for the Boussinesq equation and the Fourier symbol corresponding to the eigenvalues problem for the KdV equation, we show nonexistence of eigenvalues with respect to weighted space in a planar region containing the right-half plane. 相似文献
143.
H. Majidian 《Numerical Functional Analysis & Optimization》2013,34(6):728-737
We consider the eigenvalue problem of certain kind of noncompact linear operators given as the sum of a multiplication and a kernel operator. Under the assumption that there is a unique (up to normalization) positive eigenfunction f p , we propose a combination of the finite section and Nyström methods for approximation of f p and the corresponding eigenvalue. It is proved that the proposed method is convergent. Some examples of the problem are solved numerically using the proposed method. 相似文献
144.
145.
Qing-Ming Cheng Hongcang Yang 《Transactions of the American Mathematical Society》2006,358(6):2625-2635
Let be a connected bounded domain in an -dimensional Euclidean space . Assume that are eigenvalues of a clamped plate problem or an eigenvalue problem for the Dirichlet biharmonic operator: Then, we give an upper bound of the -th eigenvalue in terms of the first eigenvalues, which is independent of the domain , that is, we prove the following: Further, a more explicit inequality of eigenvalues is also obtained.
146.
Let T be an integer with T?5 and let T2={2,3,…,T}. We consider the nonlinear discrete boundary value problem
147.
In this paper, we present and apply a computer-assisted method to study steady states of a triangular cross-diffusion system. Our approach consist in an a posteriori validation procedure, that is based on using a fixed point argument around a numerically computed solution, in the spirit of the Newton–Kantorovich theorem. It allows to prove the existence of various non homogeneous steady states for different parameter values. In some situations, we obtain as many as 13 coexisting steady states. We also apply the a posteriori validation procedure to study the linear stability of the obtained steady states, proving that many of them are in fact unstable. 相似文献
148.
We propose and analyze a C^0 spectral element method for a model eigenvalue problem with discontinuous coefficients in the one dimensional setting. A super-geometric rate of convergence is proved for the piecewise constant coefficients case and verified by numerical tests. Furthermore, the asymptotical equivalence between a Gauss-Lobatto collocation method and a spectral Galerkin method is established for a simplified model. 相似文献
149.
In this paper an analytical procedure is given to study the free vibration and stability characteristics of homogeneous and non-homogeneous orthotropic truncated and complete conical shells with clamped edges under uniform external pressures. The non-homogeneous orthotropic material properties of conical shells vary continuously in the thickness direction. The governing equations according to the Donnell’s theory are solved by Galerkin’s method and critical hydrostatic and lateral pressures and fundamental natural frequencies have been found analytically. The appropriate formulas for homogeneous orthotropic and isotropic conical shells and for cylindrical shells made of homogeneous and non-homogeneous, orthotropic and isotropic materials are found as a special case. Several examples are presented to show the accuracy and efficiency of the formulation. The closed-form solutions are verified by accurate different solutions. Finally, the influences of the non-homogeneity, orthotropy and the variations of conical shells characteristics on the critical lateral and hydrostatic pressures and natural frequencies are investigated, when Young’s moduli and density vary together and separately. The results obtained for homogeneous cases are compared with their counterparts in the literature. 相似文献
150.
Yongjun Liu Nur Fadhilah Ibrahim 《Journal of Computational and Applied Mathematics》2010,235(1):286-292
In this paper we propose an iterative method to calculate the largest eigenvalue of a nonnegative tensor. We prove this method converges for any irreducible nonnegative tensor. We also apply this method to study the positive definiteness of a multivariate form. 相似文献