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Translated from Matematicheskie Zametki, Vol. 52, No. 5, pp. 83–87, November, 1992.  相似文献   

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We consider the Cauchy problem for the damped wave equation with absorption
(∗)  相似文献   

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We obtain asymptotic formulas for the solutions of the one-dimensional Schrödinger equation ? y″ +q(x)y = 0 with oscillating potential q(x)=x β P(x 1+α)+cx ?2 as x→ +∞. The real parameters α and β satisfy the inequalities β ? α ≥ ?1, 2α ? β > 0 and c is an arbitrary real constant. The real function P(x) is either periodic with period T, or a trigonometric polynomial. To construct the asymptotics, we apply the ideas of the averaging method and use Levinson’s fundamental theorem.  相似文献   

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In this paper we consider the Lane–Emden problem adapted for the p-Laplacian
where Ω is a bounded domain in , n ≥ 2, λ > 0 and p < qp* (with if p < n, and p* = ∞ otherwise). After some recalls about the existence of ground state and least energy nodal solutions, we prove that, when qp, accumulation points of ground state solutions or of least energy nodal solutions are, up to a “good” scaling, respectively first or second eigenfunctions of  −Δ p . Received: 29 April 2008  相似文献   

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In this note we give an answer to an open question posed by Marshall and Olkin on the majorization between the diagonal elements and the eigenvalues of an oscillating matrix.  相似文献   

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We find the first few terms of the asymptotic expansion of a regular solution of the two-dimensional Signorini problem with a small coefficient of friction. As the fundamental approximation we take the solution of the limiting problem without friction. This solution is assumed to be known, and it is assumed that the region of contact consists of a finite number of arcs, on each of which one boundary condition or another is realized. We study the asymptotics of the solution of the Signorini problem without friction under small load variation. Bibliography: 12 titles.Translated fromProblemy Matematicheskogo Analiza, No. 12, 1992, pp. 82–110.  相似文献   

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We prove the completeness of the Floquet solutions to the parabolic equation describing small oscillations of a fluid-solid system. The symmetry axis of the solid is fixed inside a container of an arbitrary shape which is filled with an incompressible viscous fluid. The solid oscillates torsionally under the action of an elastic force with time periodic rigidity.  相似文献   

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We writef=(g) iff(x)cg(x) with some positive constantc for allx from the domain of functionsf andg. We show that at least (n 2 /r) entries must be changed in an arbitrary (generalized) Hadamard matrix in order to reduce its rank belowr. This improves the previously known bound (n 2/r 2). If we additionally know that the changes are bounded above in absolute value by some numbern/r, then the number of these entries is bounded below by (n 3/(r 2 )), which improves upon the previously known bound (n 2 / 2 ).Translated fromMatematicheskie Zametki, Vol. 63, No. 4, pp. 535–540, April, 1998.The research of the first author was supported by the Russian Foundation for Basic Research under grants No. 96-01-00094 and No. 96-15-96102 and by the INTAS Foundation under grant No. 93-1376. The research of the second author was supported by the Russian Foundation for Basic Research under grants No. 96-01-01222 and No. 96-15-96090.  相似文献   

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Experimental Division, Institute for Sea Hydrophysics, Ukrainian Academy of Sciences. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 27, No. 4, pp. 78–81, October–December, 1993.  相似文献   

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This paper is concerned with the blow-up solutions of nonlinear Schrödinger equation (NLS) with oscillating nonlinearities. The limiting profiles of the blow-up solutions u(t, x) with initial data \({\|u_0\|_{L^2}=\|Q\|_{L^2}}\) are obtained. It reads that \({|u(t,x)|^2\rightarrow \|Q\|_{L^2}^2\delta_{x=y_1}}\) (Dirac function), as \({t \rightarrow T}\) , and that u(t, x) converges strongly to Q(x) in the energy space \({\Sigma=\{u\in H^1; \int |x|^2|u|^2dx<\infty\}}\) up to scaling and phase parameters and also translation in the nonradial case.  相似文献   

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High-order asymptotics is constructed and justified for optimal control over parabolic systems with rapidly oscillating coefficients in the principal part that describes high-intensity heat transfer processes in inhomogeneous and periodic media. The investigation is based on the use of methods of multiscale asymptotic decomposition and some results of the theory of averaging.  相似文献   

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For the Boltzmann equation with small transfer of momentum, we derive a system of nonlinear integral-differential equations describing the logarithmic asymptotics of the solution to the Cauchy problem in the domain at the distanceO(1) from the support of the initial condition.Translated fromMatematicheskie Zametki, Vol. 64, No. 1, pp. 73–94, July, 1998.This research was partially supported by INTAS-RFBR under grant No. 95-91 in the case of the first author, and by INTAS under grant No. 96-0698 in the case of the second author.  相似文献   

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Exact solutions of a nonlinear integro-differential equation with quadratically cubic nonlinear term are found. The equation governs, in particular, stationary shock wave propagation in relaxing media. For the exponential kernel the shapes of both compression and rarefaction shocks having a finite width of the front are calculated. For media with limited “memorizing time” the difference relation permitting the construction of wave profile by the mapping method is derived. The initial equation is rather general. It governs the evolution of nonlinear waves in real distributed systems, for example, in biological tissues, structurally inhomogeneous media and in some meta-materials.  相似文献   

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We study the decomposability of a regular matrix polynomial A(x)=A0x3+A1xs–7+.+As with commuting coefficients into factors under the assumption that some coefficient At has one of the following properties: At has only one elementary divisor; all the characteristic roots of the matrix At have multiplicity at most two.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 32, 1990, pp. 20–23.  相似文献   

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Limit spectral problems are derived for the problem on oscillations of a solid with small heavy (or light) inclusions. The asymptotic ansatzs for eigenvalues and eigenvectors, as well as the limit problems, are crucially dependent on both the relation between the geometric and physical parameters and the disposition of the inclusions. It is established that, for heavy inclusions, the limit problems are united into a more complex resultant problem describing the “far action” in the set of inclusions. Bibliography: 39 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 342, 2007, pp. 31–76.  相似文献   

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