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)).
We construct an asymptotic solution of the first boundary-value problem for a linear singularly perturbed system of hyperbolic partial differential equations with degeneration.
We construct an asymptotic solution of the first boundary-value problem for a linear singularly perturbed system of hyperbolic partial differential equations with degeneration.
In this paper we investigate the behavior and the existence of positive and non-radially symmetric solutions to nonlinear exponential elliptic model problems defined on a solid torus (T) over bar of R-3, when data are...
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In this paper we investigate the behavior and the existence of positive and non-radially symmetric solutions to nonlinear exponential elliptic model problems defined on a solid torus (T) over bar of R-3, when data are invariant under the group G = 0(2) x I subset of 0(3). The model problems of interest are stated below: Delta v + y = f(x)e(v), v>0 on T, v vertical bar partial derivative T=0 (P-1) and Delta v + a + f e(v) = 0, v > 0 on T, partial derivative v/partial derivative n + b + ge(v) = 0 on partial derivative T. (P-2) We prove that exist solutions which are G-invariant and these exhibit no radial symmetries. In order to solve the above problems we need to find the best constants in the Sobolev inequalities in the exceptional case. (C) 2011 Elsevier Inc. All rights reserved.
We consider a quasilinear parabolic boundaryvalue problem of the third kind on an interval. The coefficients of the partial differential equation and the right-hand sides in the boundary conditions and the evolution ...
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We consider a quasilinear parabolic boundaryvalue problem of the third kind on an interval. The coefficients of the partial differential equation and the right-hand sides in the boundary conditions and the evolution equation for the state vector nonlinearly depend on time, the point, the state vector, and the values of the solution at the endpoints. This problem generalizes a number of models of formation and decomposition of metal hydrides. For the simplest finite-difference scheme, we prove the uniform convergence to a continuous generalized solution of the boundaryvalue problem. A sample model is given.
The Riemann boundary-value problem is solved for the classes of open rectifiable Jordan curves extended as compared with previous results and functions defined on these curves.
The Riemann boundary-value problem is solved for the classes of open rectifiable Jordan curves extended as compared with previous results and functions defined on these curves.
In this article, a meshless numerical algorithm is proposed for the boundary identification problem of heat conduction, one kind of inverse problem. In the geometry boundary identification problem, the Cauchy data is ...
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In this article, a meshless numerical algorithm is proposed for the boundary identification problem of heat conduction, one kind of inverse problem. In the geometry boundary identification problem, the Cauchy data is given for part of the boundary. The Neumann boundary condition is given for the other portion of the boundary, whose spatial position is unknown. In order to stably solve the inverse problem, the modified collocation Trefftz method, a promising boundary-type meshless method, is adopted for discretizing this problem. Since the spatial position for part of the boundary is unknown, the numerical discretization results in a system of nonlinear algebraic equations (NAEs). Then, the exponentially convergent scalar homotopy algorithm (ECSHA) is used to efficiently obtain the convergent solution of the system of NAEs. The ECSHA is insensitive to the initial guess of the evolutionary process. In addition, the efficiency of the computation is greatly improved, since calculation of the inverse of the Jacobian matrix can be avoided. Four numerical examples are provided to validate the proposed meshless scheme. In addition, some factors that might influence the performance of the proposed scheme are examined through a series of numerical experiments. The stability of the proposed scheme can be proven by adding some noise to the boundary conditions.
A study was conducted to investigate various aspects of using the block element method and demonstrate its application to particular boundary-valueproblems. It was shown that the block element method made it possible...
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A study was conducted to investigate various aspects of using the block element method and demonstrate its application to particular boundary-valueproblems. It was shown that the block element method made it possible to obtain the exact solution contrary to other numerical approaches a priori aimed at constructing an approximate solution of the boundary-value problem. other functions were determined in the block element method contrary to the variable-division method when the functions directly describing the solution of the boundary-value problem were found from the set boundary conditions. Another feature of the method was the circumstance that the variable-division method allowed one to construct the solution of the boundary-value problem.
This work is devoted to the optimal and a posteriori error estimates of the Stokes problem with some non-standard boundary conditions in three dimensions. The variational formulation is decoupled into a system for the...
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This work is devoted to the optimal and a posteriori error estimates of the Stokes problem with some non-standard boundary conditions in three dimensions. The variational formulation is decoupled into a system for the velocity and a Poisson equation for the pressure. The velocity is approximated with curl conforming finite elements and the pressure with standard continuous elements. Next, we establish optimal a posteriori estimates. (C) 2011 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.
Let T be a torsion abelian group. We consider the class of all torsion-free abelian groups G satisfying Ext(G, T) = 0 and search for lambda-universal objects in this class. We show that, for certain T, there is no ome...
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Let T be a torsion abelian group. We consider the class of all torsion-free abelian groups G satisfying Ext(G, T) = 0 and search for lambda-universal objects in this class. We show that, for certain T, there is no omega-universal group. However, for uncountable cardinals lambda there is always a lambda-universal group if we assume (V = L). Together with results by the second author this solves completely a problem by Kulikov.
We study the boundary-value problem of determining the parameter p of a parabolic equation v'(t) + Av(t) = f(t) + p, 0 <= t <= 1, v(0) = phi, v(1) = psi, with strongly positive operator A in an arbitrary Ban...
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We study the boundary-value problem of determining the parameter p of a parabolic equation v'(t) + Av(t) = f(t) + p, 0 <= t <= 1, v(0) = phi, v(1) = psi, with strongly positive operator A in an arbitrary Banach space E: The exact estimates are established for the solution of this problem in Holder norms. In applications, the exact estimates are obtained for the solutions of the boundary-valueproblems for parabolic equations.
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