共查询到20条相似文献,搜索用时 15 毫秒
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A reaction-diffusion system of activator-inhibitor type is studied on an N-dimensional ball with the homogeneous Neumann boundary conditions. We analyze the stability property of the spherically symmetric solutions and their symmetry-breaking bifurcations into layer solutions which are not spherically symmetric. 相似文献
3.
We prove global existence of nonnegative weak solutions to a degenerate parabolic system which models the interaction of two thin fluid films in a porous medium. Furthermore, we show that these weak solutions converge at an exponential rate towards flat equilibria. 相似文献
4.
Reaction-diffusion systems of activator-inhibitor type are studied on an N-dimensional ball with the homogeneous Neumann boundary conditions. Under the condition that the activator diffuses slowly, reacts rapidly and the inhibitor diffuses rapidly, reacts moderately, we show that the system admits a family of spherically symmetric internal transition layer equilibria. The method of proof consists of rigorous asymptotic expansions and a Lyapunov-Schmidt reduction. 相似文献
5.
Amin Esfahani 《Journal of Differential Equations》2009,247(12):3181-323
In this paper we study the generalized BO-ZK equation in two space dimensions
ut+upux+αHuxx+εuxyy=0. 相似文献
6.
M. Sango 《Integral Equations and Operator Theory》2002,43(2):177-188
We consider the spectral problem for a non self-adjoint Dirichlet problem for a higher-order elliptic operator in a sequence of perforated domains. We establish the convergence of the singular numbers generated by the problem to the corresponding singular numbers generated by a limit problem of the same type but containing an additional term of capacity type.Research supported by the National Research Foundation of South Africa. 相似文献
7.
Mathew A. Johnson 《Journal of Differential Equations》2010,249(5):1213-1310
Extending previous results of Oh-Zumbrun and Johnson-Zumbrun, we show that spectral stability implies linearized and nonlinear stability of spatially periodic traveling wave solutions of viscous systems of conservation laws for systems of generic type, removing a restrictive assumption that wave speed be constant to first order along the manifold of nearby periodic solutions. Key to our analysis is a nonlinear cancellation estimate observed by Johnson and Zumbrun, along with a detailed understanding of the Whitham averaged system. The latter motivates a careful analysis of the Bloch perturbation expansion near zero frequency and suggests factoring out an appropriate translational modulation of the underlying wave, allowing us to derive the sharpened low-frequency estimates needed to close the nonlinear iteration arguments. 相似文献
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O. Jokhadze 《Georgian Mathematical Journal》1995,2(5):469-490
A Darboux type problem for a model hyperbolic equation of the third order with multiple characteristics is considered in the case of two independent variables. The Banach space, 0, is introduced where the problem under consideration is investigated. The real number 0 is found such that for > 0 the problem is solved uniquely and for < 0 it is normally solvable in Hausdorff's sense. In the class of uniqueness an estimate of the solution of the problem is obtained which ensures stability of the solution. 相似文献
9.
JIANGLISHANG LIUZUHAN YIFAHUAI YUEXINGYE 《高校应用数学学报(英文版)》1995,10(1):1-10
This paper deals with the relationship between a certain three-dimensional elliptic problem and a two-dimensional parabolic problem, which arises from numerical calculation in the process of the continuous casting of steel. 相似文献
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S. Kharibegashvili 《Georgian Mathematical Journal》1994,1(2):141-150
A theorem of the unique solvability of the first boundary value problem in the Sobolev weighted spaces is proved for higherorder strictly hyperbolic systems in the conic domain with special orientation. 相似文献
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Youshan Tao 《Journal of Differential Equations》2009,247(1):49-68
This paper deals with a mathematical model describing the cell cycle dynamics and chemotactic driven cell movement in a multicellular tumor spheroid. Tumor cells consist of two types of cells: proliferating cells and quiescent cells, which have different chemotactic responses to an extracellular nutrient supply. The model is a free boundary problem for a nonlinear system of reaction-diffusion-advection equations, where the free boundary is the outer boundary of the spheroid. The free boundary condition is quite novel due to different velocity of two types of cells. The global existence and uniqueness of solutions to the model is proved. The proof is based on a fixed point argument, together with the Lp-theory for parabolic equations with the third boundary condition. 相似文献
12.
Z. Brzeźniak T. Caraballo J.A. Langa Y. Li G. Łukaszewicz J. Real 《Journal of Differential Equations》2013
We show that the stochastic flow generated by the 2-dimensional Stochastic Navier–Stokes equations with rough noise on a Poincaré-like domain has a unique random attractor. One of the technical problems associated with the rough noise is overcomed by the use of the corresponding Cameron–Martin (or reproducing kernel Hilbert) space. Our results complement the result by Brze?niak and Li (2006) [10] who showed that the corresponding flow is asymptotically compact and also generalize Caraballo et al. (2006) [12] who proved existence of a unique attractor for the time-dependent deterministic Navier–Stokes equations. 相似文献
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By using the I-method, we prove that the Cauchy problem of the fifth-order shallow water equation is globally well-posed in the Sobolev space Hs(R) provided . 相似文献
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The initial boundary value problem for non-linear wave equations of Kirchhoff type with dissipation in a bounded domain is considered. We prove the blow-up of solutions for the strong dissipative term -Δut and the linear dissipative term ut by the energy method and give some estimates for the life span of solutions. We also show the nonexistence of global solutions with positive initial energy for non-linear dissipative term by Vitillaro's argument. 相似文献
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Mitsuhiro Nakao 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(7):2158-2169
We derive an energy decay estimate for solutions to the initial-boundary value problem of a semilinear wave equation with a nonlinear localized dissipation. To overcome a difficulty related to derivative-loss mechanism we employ a ‘loan’ method. 相似文献
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L.M. Bragança 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(9):2991-3003
We investigate some well-posedness issues for the initial value problem (IVP) associated with the system
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This paper is concerned with the existence, uniqueness, and nonlinear stability of stationary solutions to the Cauchy problem of the full compressible Navier–Stokes–Korteweg system effected by the given mass source, the external force of general form, and the energy source in R3. Based on the weighted L2-method and some delicate L∞ estimates on solutions to the linearized problem, the existence and uniqueness of stationary solution are obtained by the contraction mapping principle. The proof of the stability result is given by an elementary energy method and relies on some intrinsic properties of the full compressible Navier–Stokes–Korteweg system. 相似文献
18.
We consider Neumann initial-boundary value problem for the Korteweg-de Vries equation on a half-line
(0.1) 相似文献
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Futoshi Takahashi 《Calculus of Variations and Partial Differential Equations》2007,29(4):509-520
We continue to study the asymptotic behavior of least energy solutions to the following fourth order elliptic problem (E
p
): as p gets large, where Ω is a smooth bounded domain in R
4
. In our earlier paper (Takahashi in Osaka J. Math., 2006), we have shown that the least energy solutions remain bounded uniformly
in p and they have one or two “peaks” away form the boundary. In this note, following the arguments in Adimurthi and Grossi (Proc.
AMS 132(4):1013–1019, 2003) and Lin and Wei (Comm. Pure Appl. Math. 56:784–809, 2003), we will obtain more sharper estimates
of the upper bound of the least energy solutions and prove that the least energy solutions must develop single-point spiky
pattern, under the assumption that the domain is convex. 相似文献
20.
We show that there is a class of solutions to the generalized Proudman-Johnson equation which exist globally for all parameters a having the form for n∈N, thereby extending a result of Bressan and Constantin (2005) [2]. Furthermore, we present new proofs of existence of solutions developing spontaneous singularities and compute the corresponding blow-up rates. 相似文献