共查询到20条相似文献,搜索用时 15 毫秒
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Snorre H. Christiansen. 《Mathematics of Computation》2004,73(245):143-167
The Galerkin discretization of the Electric Field Integral Equation is reinvestigated. We prove quasi-optimal convergence estimates at nonresonant frequencies, using orthogonal splittings of the Galerkin space. At resonant frequencies we show that the spurious electric currents radiate only weakly in the exterior domain. This is achieved through the study of some finitely degenerated problems in terms of LBB Inf-Sup estimates and the use of discrete Helmholtz decompositions.
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An initial problem is considered for an ordinary singularly perturbed integro-differential equation with a nonlinear integral Fredholm operator. The case when the reduced equation has a smooth solution is investigated, and the solution to the reduced equation with a corner point is analyzed. The asymptotics of the solution to the Cauchy problem is constructed by the method of boundary functions. The asymptotics is validated by the asymptotic method of differential inequalities developed for a new class of problems. 相似文献
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V. I. Ovchinnikov 《Mathematical Notes》1971,10(5):749-753
We prove that for any Fredholm operator A(x) of class C1 and zero index in a Hilbert space, in a neighborhood of any star compactum T lying in the domain of A we can define a completely continuous and continuously differentiable operator C, so that the linear operator A(x)+ C(x) has a bounded inverse for all xT.Translated from Matematicheskie Zametki, Vol. 10, No. 5, pp. 541–548, November, 1971.The author wishes to thank M. A. Krasnosel'skii for posing the problem, and P. P. Zabreiko and S. G. Krein for their interest in this work. 相似文献
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We consider a spectral problem that is nonlinear in the spectral parameter for a self-adjoint vector differential equation of order 2n. The boundary conditions depend on the spectral parameter and are self-adjoint as well. Under some conditions of monotonicity of the input data with respect to the spectral parameter, we present a method for counting the eigenvalues of the problem in a given interval. If the boundary conditions are independent of the spectral parameter, then we define the notion of number of an eigenvalue and give a method for computing this number as well as the set of numbers of all eigenvalues in a given interval. For an equation considered on an unbounded interval, under some additional assumptions, we present a method for approximating the original singular problem by a problem on a finite interval. 相似文献
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In a Hilbert space H, we study the Fredholm property of a boundary value problem for a fourth-order differential-operator equation of elliptic type with unbounded operators in the boundary conditions. We find sufficient conditions on the operators in the boundary conditions for the problem to be Fredholm. We give applications of the abstract results to boundary value problems for fourth-order elliptic partial differential equations in nonsmooth domains. 相似文献
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Sh. Yarmukhamedov 《Mathematical Notes》1975,18(1):615-618
We obtain a formula which expresses the values of a harmonic function at points of a threedimensional domain in terms of its values and the values of its normal derivative on a portion of the domain boundary. 相似文献
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Yu. A. Mitropol'skii M. Kh. Shkhanukov A. A. Berezovskii 《Ukrainian Mathematical Journal》1995,47(6):911-923
We study a nonlocal boundary-value problem for a parabolic equation in a two-dimensional domain, establish ana priori estimate in the energy norm, prove the existence and uniqueness of a generalized solution from the classW
2
1,0
(Q
T
), and construct a difference scheme for the second-order approximation.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 6, pp. 790–800, June, 1995. 相似文献
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Qun Lin Yong Hong Wu Ryan Loxton 《Journal of Mathematical Analysis and Applications》2009,353(1):186-4258
In this paper, we consider the Cauchy problem for a generalized Boussinesq equation. We show that, under suitable conditions, a global solution for the initial value problem exists. In addition, we derive the sufficient conditions for the blow-up of the solution to the problem. 相似文献
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Weikui Ye 《Applicable analysis》2020,99(8):1300-1315
ABSTRACTWe first establish the local well-posedness for a generalized Degasperis-Procesi equation in nonhomogeneous Besov spaces. Then we present a global existence result for the equation. Moreover, we obtain a blow-up criteria and provide a sufficient condition for strong solutions to blow up in finite time. 相似文献
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Summary The explicit solution of a particularCauchy problem for the n-dimensionalEuler-Poisson-Darboux equation is found. To obtain the solution the method ofM. Riesz is extended to include non self-adjoint equations. Existence and uniqueness are shown.
This research was supported in part by the United States Air Force under Contract No. AF18(600)-573 — monitored by the Office
of Scientific Research, Air Research and Development Command. 相似文献
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By analyzing a system of integro-differential equations of the Volterra-Stieltjes type, for large parameter values, we obtain asymptotic formulas for a linearly independent system of solutions of ordinary differential equations with generalized functions in coefficients. These solutions permit one to construct asymptotic formulas for the eigenvalues of a boundary value problem in the case of regular boundary conditions. 相似文献
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We state a new nonlocal boundary value problem for a mixed parabolic-hyperbolic equation. The equation is of the first kind, i.e., the curve on which the equation changes type is not a characteristic. The nonlocal condition involves points in hyperbolic and parabolic parts of the domain. This problem is a generalization of the well-known Frankl-type problems. Unlike other close publications, the hyperbolic part of the domain agrees with a characteristic triangle. We prove unique solvability of this problem in the sense of classical and strong solutions. 相似文献