共查询到20条相似文献,搜索用时 0 毫秒
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《Nonlinear Analysis: Real World Applications》2007,8(3):1013-1023
We shall consider an interfacial problem arising reaction–diffusion models with inhomogeneous media. The purpose of this paper is to analyze the occurrence of Hopf bifurcation in the interfacial problem and to examine the effects of an inhomogeneous media. Conditions for existence of stationary solutions and Hopf bifurcation for a certain class of inhomogeneity are obtained analytically and numerically. 相似文献
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In this paper, we prove a bifurcation phenomenon in a two-phase, singularly perturbed, free boundary problem of phase transition. We show that the uniqueness of the solution for the two-phase problem breaks down as the boundary data decreases through a threshold value. For boundary values below the threshold, there are at least three solutions, namely, the harmonic solution which is treated as a trivial solution in the absence of a free boundary, a nontrivial minimizer of the functional under consideration, and a third solution of the mountain-pass type. We classify these solutions according to the stability through evolution. The evolution with initial data near a stable solution, such as the trivial harmonic solution or a minimizer of the functional, converges to the stable solution. On the other hand, the evolution deviates away from a non-minimal solution of the free boundary problem. 相似文献
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In this paper, a free boundary problem modeling tumor growth with two discrete delays is studied. The delays respectively represents the time taken for cells to undergo mitosis and the time taken for the cell to modify the rate of cell loss due to apoptosis. We show the influence of time delays on the Hopf bifurcation when one of delays as a bifurcation parameter. 相似文献
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We consider a free boundary problem for a system of partial differential equations, which arises in a model of tumor growth. For any positive number there exists a radially symmetric stationary solution with free boundary . The system depends on a positive parameter , and for a sequence of values there also exist branches of symmetric-breaking stationary solutions, parameterized by , small, which bifurcate from these values. In particular, for near the free boundary has the form where is the spherical harmonic of mode . It was recently proved by the authors that the stationary solution is asymptotically stable for any , but linearly unstable if , where if and if ; . In this paper we prove that for each of the stationary solutions which bifurcates from is linearly stable if and linearly unstable if . We also prove, for , that the point is a Hopf bifurcation, in the sense that the linearized time-dependent problem has a family of solutions which are asymptotically periodic in .
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Antoine Henrot 《Arkiv f?r Matematik》1994,32(1):79-98
We begin by giving some results of continuity with respect to the domain for the Dirichlet problem (without any assumption
of regularity on the domains). Then, following an idea of A. Beurling, a technique of subsolutions and supersolutions for
the so-called quadrature surface free boundary problem is presented. This technique would apply to many free boundary problems
inR
N,N≥2, which have overdetermined Cauchy data on the free boundary. Some applications to concrete examples are also given.
This work was done while the author was at the University of Nancy I (France) supported by URA 750 CNRS and project Numath
INRIA Lorraine. 相似文献
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G. A. Philippin 《Mathematical Methods in the Applied Sciences》1990,12(5):387-392
Let Ωi ? ?N, i = 0, 1, be two bounded separately star-shaped domains such that $ \Omega _0 \supset \bar \Omega _1 $. We consider the electrostatic potential u defined in $ \Omega : = \Omega _0 \backslash \bar \Omega _1 $: The geometry of the two boundary components Γ0 and Γ1 is not given, but instead the electrostatic potential u is supposed to satisfy the further boundary conditions Using a best possible maximum principle, we show that this free boundary problem has a unique solution which is radially symmetric. 相似文献
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Let u be the Newtonian potential of a real analytic distribution in an open set Ω. In this paper we assume u is analytically
continuable from the complement of Ω into some neighborhood of a point x0 ∈ ∂Ω, and we study conditions under which the analytic continuation implies that ∂Ω is a real analytic hypersurface in some
neighborhood of x0. 相似文献
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Grzegorz ukaszewicz Witold Sadowski 《Mathematical Methods in the Applied Sciences》2000,23(12):1023-1035
We consider a boundary value problem describing the stationary flow of a non‐Newtonian fluid through the frozen ground, with a free interface between the liquid and the solid phases. We prove the existence of at least one weak solution of the problem. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献
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Yong Liu Kelei Wang Juncheng Wei 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2018,35(4):993-1017
From minimal surfaces such as Simons' cone and catenoids, using refined Lyapunov–Schmidt reduction method, we construct new solutions for a free boundary problem whose free boundary has two components. In dimension 8, using variational arguments, we also obtain solutions which are global minimizers of the corresponding energy functional. This shows that the theorem of Valdinoci et al. [41], [42] is optimal. 相似文献
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In this paper, we consider a free boundary problem with volume constraint. We show that positive minimizer is locally Lipschitz
and the free boundary is analytic away from a singular set with Hausdorff dimension at most n − 8. 相似文献
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K.J. Brown 《Journal of Differential Equations》2007,239(2):296-310
We investigate the local and global nature of the bifurcation diagrams which can occur for a semilinear elliptic boundary value problem with Neumann boundary conditions involving sign-changing coefficients. It is shown that closed loops of positive and negative solutions occur naturally for such problems and properties of these loops are investigated. 相似文献
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Joachim Escher Gieri Simonett 《NoDEA : Nonlinear Differential Equations and Applications》1995,2(4):463-510
This paper is concerned with the motion of an incompressible fluid in a rigid porous medium of infinite extent. The fluid is bounded below by a fixed, impermeable layer and above by a free surface moving under the influence of gravity. The laminar flow is governed by Darcy's law.We prove existence of a unique maximal classical solution, using methods from the theory of maximal regularity, analytic semigroups, and Fourier multipliers. Moreover, we describe a state space which can be considered as domain of parabolicity for the problem under consideration.Supported by Schweizerischer Nationalfonds 相似文献
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We consider a boundary identification problem arising in nondestructive testing of materials. The problem is to recover a part ΓI⊂∂Ω of the boundary of a bounded, planar domain Ω from one Cauchy data pair (u,∂u/∂ν) of a harmonic potential u in Ω collected on an accessible boundary subset ΓA⊂∂Ω. We prove Fréchet differentiability of a suitably defined forward map, and discuss local uniqueness and Lipschitz stability results for the linearized problem. 相似文献
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M. Poghosyan R. Teymurazyan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2009,44(3):192-204
This paper studies a free boundary problem for the heat equation in a convex ring. It is proved that the considered problem has unique solution under some conditions on the initial data. 相似文献
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