共查询到20条相似文献,搜索用时 15 毫秒
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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
3.
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
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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
5.
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
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
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Thierry Cazenave Flávio Dickstein Fred B. Weissler 《Journal of Differential Equations》2009,246(7):2669-568
In this paper, given 0<α<2/N, we prove the existence of a function ψ with the following properties. The solution of the equation ut−Δu=α|u|u on RN with the initial condition u(0)=ψ is global. On the other hand, the solution with the initial condition u(0)=λψ blows up in finite time if λ>0 is either sufficiently small or sufficiently large. 相似文献
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V. V. Pukhnachov 《Acta Appl Math》1994,37(1-2):147-152
Stationary solutions of free boundary problems for the Navier-Stokes equations are considered with and without surface tension. The linearized problem in a half-space is studied. Exact solutions of the Poiseuille type are obtained. Properties of the free boundary smoothness in 3-D and 2-D cases are discussed. 相似文献
9.
Masaharu Taniguchi 《Journal of Differential Equations》2009,246(5):2103-2424
This paper studies the uniqueness and the asymptotic stability of a pyramidal traveling front in the three-dimensional whole space. For a given admissible pyramid we prove that a pyramidal traveling front is uniquely determined and that it is asymptotically stable under the condition that given perturbations decay at infinity. For this purpose we characterize the pyramidal traveling front as a combination of planar fronts on the lateral surfaces. Moreover we characterize the pyramidal traveling front in another way, that is, we write it as a combination of two-dimensional V-form waves on the edges. This characterization also uniquely determines a pyramidal traveling front. 相似文献
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Mitsuhiro Nakao 《Nonlinear Analysis: Theory, Methods & Applications》2012,75(4):2236-2248
We prove the global existence of the so-called H2 solutions for a nonlinear wave equation with a nonlinear dissipative term and a derivative type nonlinear perturbation. To show the boundedness of the second order derivatives we need a precise energy decay estimate and for this we employ a ‘loan’ method. 相似文献
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R.R. Carvalho M. Milla Miranda 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(7):2101-2116
This paper is concerned with the study of the existence and decay of solutions of the following initial value problem:
(∗) 相似文献
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First, we introduce the concept of pullback asymptotically compact non-autonomous dynamical system as an extension of the similar concept in the autonomous framework. Our definition is different from that of asymptotic compactness already used in the theory of random and non-autonomous dynamical systems (as developed by Crauel, Flandoli, Kloeden, Schmalfuss, amongst others) which means the existence of a (random or time-dependent) family of compact attracting sets. Next, we prove a result ensuring the existence of a pullback attractor for a non-autonomous dynamical system under the general assumptions of pullback asymptotic compactness and the existence of a pullback absorbing family of sets. This attractor is minimal and, in most practical applications, it is unique. Finally, we illustrate the theory with a 2D Navier–Stokes model in an unbounded domain. 相似文献
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Erik Wahlén 《NoDEA : Nonlinear Differential Equations and Applications》2007,13(5-6):643-653
We prove a blow-up result for a nonlinear shallow water equation by showing that certain initial profiles evolve into breaking
waves. 相似文献
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A. V. Kazhikhov 《Acta Appl Math》1994,37(1-2):77-81
The existence, uniqueness, and stabilization of solutions are investigated for two approximate models of viscous compressible fluid. 相似文献
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In the paper, we first use the energy method to establish the local well-posedness as well as blow-up criteria for the Cauchy problem on the two-component Euler–Poincaré equations in multi-dimensional space. In the case of dimensions 2 and 3, we show that for a large class of smooth initial data with some concentration property, the corresponding solutions blow up in finite time by using Constantin–Escher Lemma and Littlewood–Paley decomposition theory. Then for the one-component case, a more precise blow-up estimate and a global existence result are also established by using similar methods. Next, we investigate the zero density limit and the zero dispersion limit. At the end, we also briefly demonstrate a Liouville type theorem for the stationary weak solution. 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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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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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
20.
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