共查询到20条相似文献,搜索用时 0 毫秒
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Ukrainian Mathematical Journal - 相似文献
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The Cauchy problem for a second-order Petrovskii parabolic system with bounded and continuous coefficients that are Dini-continuous with respect to space variables is proved to have a unique classical solution in the Tikhonov class. 相似文献
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This paper concerns the uniqueness of the bounded solution to a strongly degenerate parabolic problem. The equation considered may have two kinds of strong degeneracies and there is no restriction on the relation between the two degeneracies. By using Holmgren’s approach, we prove that the bounded solution of the associated initial–boundary value problem is unique under some essentially necessary condition on the growth of the convection. 相似文献
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C. Lederman J. L. Vá zquez N. Wolanski 《Transactions of the American Mathematical Society》2001,353(2):655-692
We investigate the uniqueness and agreement between different kinds of solutions for a free boundary problem in heat propagation that in classical terms is formulated as follows: to find a continuous function defined in a domain and such that
0\}. \end{displaymath}">
We also assume that the interior boundary of the positivity set, \nobreak 0\}$">, so-called free boundary, is a regular hypersurface on which the following conditions are satisfied:
Here denotes outward unit spatial normal to the free boundary. In addition, initial data are specified, as well as either Dirichlet or Neumann data on the parabolic boundary of . This problem arises in combustion theory as a limit situation in the propagation of premixed flames (high activation energy limit).
The problem admits classical solutions only for good data and for small times. Several generalized concepts of solution have been proposed, among them the concepts of limit solution and viscosity solution. We investigate conditions under which the three concepts agree and produce a unique solution.
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V. A. Kozlov V. G. Maz’ya A. V. Fomin 《Computational Mathematics and Mathematical Physics》2009,49(3):525-531
The inverse problem of coupled thermoelasticity is considered in the static, quasi-static, and dynamic cases. The goal is to recover the thermal stress state inside a body from the displacements and temperature given on a portion of its boundary. The inverse thermoelasticity problem finds applications in structural stability analysis in operational modes, when measurements can generally be conducted only on a surface portion. For a simply connected body consisting of a mechanically and thermally isotropic linear elastic material, uniqueness theorems are proved in all the cases under study. 相似文献
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V. N. Starovoitov 《Siberian Mathematical Journal》1994,35(3):625-630
Translated from Sibirskii Matematicheskii, Vol. 35, No. 3, pp. 696–701, May–June, 1994. 相似文献
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Massimo Grossi 《Proceedings of the American Mathematical Society》2000,128(6):1665-1672
We prove that the least-energy solution of the problem
where is a ball, and if , if , is unique (up to rotation) if is small enough.
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V. I. Gishlarkaev 《Journal of Mathematical Sciences》2010,169(1):64-83
We consider the Cauchy problem for the Hopf equation corresponding to the two-dimensional Navier–Stokes equations. The global
uniqueness of a solution is proved under the condition that the mean energy of the initial measure is finite, without any
additional conditions, i.e., under the same assumptions as in the existence theorem. Thereby we receive a sharp improvement
of Foias’s result obtained in the 1970’s about the uniqueness of a spatial statistical solution. Bibliography: 12 titles. 相似文献
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Ernesto Prado Lopes José Roberto Linhares de Mattos 《Proceedings of the American Mathematical Society》2008,136(6):2201-2207
We consider the problem , , , where is bounded below by a positive constant. The solution on the boundary is a known function and . This is an ill-posed problem in the sense that a small disturbance on the boundary specification can produce a big change in its solution, if it exists. In a previous work, we used a Wavelet Galerkin Method with the Meyer Multiresolution Analysis to generate a sequence of well-posed approximating problems to it. In the present work, by assuming that is Lipschitz, we are able to prove that the existence of a solution , for this problem, implies its uniqueness.
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Conditions satisfied by a region of a sphere are found under which the differential equation arising in the solution of Christoffel's problem has not more than one solution in the region taking given boundary values.Translated from Matematicheskie Zametki, Vol. 8, No. 2, pp. 251–257, August, 1970. 相似文献
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