Stokes flow in a rectangular cavity with two moving lids (with equal speed but in opposite directions) and aspect ratio A (height to width) is considered. An analytic solution for the stream function, psi, expressed a...
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Stokes flow in a rectangular cavity with two moving lids (with equal speed but in opposite directions) and aspect ratio A (height to width) is considered. An analytic solution for the stream function, psi, expressed as an infinite series of Papkovich-Fadle eigenfunctions is used to reveal changes in flow structures as A is varied. Reducing A from A = 0.9 produces a sequence of flow transformations at which a saddle stagnation point changes to a centre (or vice versa) with the generation of two additional stagnation points. To obtain the local flow topology as A --> 0, we expand the velocity field about the centre of the cavity and then use topological methods. Expansion coefficients depend on the cavity aspect ratio which is considered as a separation parameter. The normal-form transformations result in a much simplified system of differential equations for the streamlines encapsulating all features of the original system. Using the simplified system, streamline patterns and their bifurcations are obtained, as A --> 0.
We study the inverse spectral problem on the half-line for the Sturm-Liouville operator with periodic potential. We derive a formula expressing the boundary condition via the spectral data and an analog of Dubrovin...
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We study the inverse spectral problem on the half-line for the Sturm-Liouville operator with periodic potential. We derive a formula expressing the boundary condition via the spectral data and an analog of Dubrovin's system of differential equations and present an algorithm for constructing the potential.
On the interval (0, pi), we consider the spectral problem generated by the Sturm-Liouville operator with regular but not strongly regular boundary conditions. For an arbitrary potential q(x) is an element of L(1) (0, ...
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On the interval (0, pi), we consider the spectral problem generated by the Sturm-Liouville operator with regular but not strongly regular boundary conditions. For an arbitrary potential q(x) is an element of L(1) (0, pi) [q(x) is an element of L(2)(0, pi)], we establish exact asymptotic formulas for the eigenvalues of this problem.
We study the numerical solution to inverse problems in which one reconstructs the coefficients of a parabolic equation depending only on one (space or time) variable. In particular, these classes of problems arise in ...
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We study the numerical solution to inverse problems in which one reconstructs the coefficients of a parabolic equation depending only on one (space or time) variable. In particular, these classes of problems arise in the study of boundaryvalueproblems with nonlocal (integral) boundary conditions. We suggest an approach to the numerical solution to these problems with the use of the line method and the reduction of the original problem to the solution to auxiliary Cauchy problems for systems of ordinary differential equations. We present the results of numerical experiments with test problems.
We first prove two theorems on the low(2) degrees and the join property in the local structure D(<= 0'): An r.e. degree is low(2) if and only if it is bounded by an r.e. degree without the join property (in D(&...
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We first prove two theorems on the low(2) degrees and the join property in the local structure D(<= 0'): An r.e. degree is low(2) if and only if it is bounded by an r.e. degree without the join property (in D(<= 0')), and an FPF Delta(0)(2) degree is low(2) if and only if it fails to have the join property. We also study the join property in the global structure and show that for every array recursive degree, there is a degree above it which fails to satisfy the join property.
In this paper, we prove the existence of infinitely many solutions for the following elliptic problem with critical Sobolev growth: -Delta u = vertical bar u vertical bar(2)*(-2)u + g(u) in Omega, partial derivative u...
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In this paper, we prove the existence of infinitely many solutions for the following elliptic problem with critical Sobolev growth: -Delta u = vertical bar u vertical bar(2)*(-2)u + g(u) in Omega, partial derivative u/partial derivative nu = 0 on partial derivative Omega, where Omega is a bounded domain in R-N with C-3 boundary, N >= 3, nu is the outward unit normal of partial derivative Omega, 2* = 2N/N-2, and g(t) = mu vertical bar t vertical bar(p-2)t - t, or g(t) = mu t, where p is an element of (2, 2*), mu > 0 are constants. We obtain the existence of infinitely many solutions under certain assumptions on N, p and partial derivative Omega. In particular, if g(t) = mu t with mu > 0, N >= 7, and Omega is a strictly convex domain, then the problem has infinitely many solutions. (C) 2011 Published by Elsevier Inc.
We consider the resource allocation problem for a two-sector economic model with a two-factor Cobb-Douglas production function on a finite time horizon with a terminal functional. The problem is reduced to some canoni...
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We consider the resource allocation problem for a two-sector economic model with a two-factor Cobb-Douglas production function on a finite time horizon with a terminal functional. The problem is reduced to some canonical form by a scaling of the phase variables and time. We prove the optimality of the extremal solution constructed on the basis of the maximum principle. The solution of the boundaryvalue problem of the maximum principle is constructed in closed form for three cases of location of the initial plant state.
By using the Krasnoselskii's fixed point theorem and operator spectral theorem, the existence of positive solutions for the nonlocal fourth-order boundaryvalue problem with variable parameter u((4)) (t) + B(t) u&...
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By using the Krasnoselskii's fixed point theorem and operator spectral theorem, the existence of positive solutions for the nonlocal fourth-order boundaryvalue problem with variable parameter u((4)) (t) + B(t) u"(t) = lambda f (t, u(t), u" (t)), 0 < t < 1, u(0) = u(1) = integral(1)(0) p(s) u (s) ds, u" (0) = u"(1) = integral(1)(0)q (s) u" (s) ds is considered, where p, q is an element of L(1) [0,1], lambda > 0 is a parameter, and B is an element of C [0, 1], f is an element of C([0, 1] x [0, infinity) x (-infinity, 0], [0, infinity)).
By employing upper and lower solutions method together with maximal principle, we establish a necessary and sufficient condition for the existence of pseudo-C(3)[0, 1] as well as C(2)[0, 1] positive solutions for four...
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By employing upper and lower solutions method together with maximal principle, we establish a necessary and sufficient condition for the existence of pseudo-C(3)[0, 1] as well as C(2)[0, 1] positive solutions for fourth-order singular p-Laplacian differential equations with integral boundary conditions. Our nonlinearity f may be singular at t = 0, t = 1, and u = 0. The dual results for the other integral boundary condition are also given.
In the present paper, we write out the eigenvalues and the corresponding eigenfunctions of the modified Frankl problem with a nonlocal parity condition of the second kind. We analyze the completeness, the basis proper...
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In the present paper, we write out the eigenvalues and the corresponding eigenfunctions of the modified Frankl problem with a nonlocal parity condition of the second kind. We analyze the completeness, the basis property, and the minimality of the eigenfunctions depending on the parameter of the problem.
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