共查询到20条相似文献,搜索用时 687 毫秒
1.
Francisco Morillas 《Topology and its Applications》2009,156(18):3029-3040
We prove the Kneser property (i.e. the connectedness and compactness of the attainability set at any time) for reaction-diffusion systems on unbounded domains in which we do not know whether the property of uniqueness of the Cauchy problem holds or not.Using this property we obtain that the global attractor of such systems is connected.Finally, these results are applied to the complex Ginzburg-Landau equation. 相似文献
2.
In this paper, we prove that the Cauchy problem to a hyperbolic conservation laws with relaxation with singular initial data admits a unique global entropy solution in the sense of Definition 1.1. Compared with former results in this direction, the main ingredient of this paper lies in the fact that it contains a uniqueness result and we do not ask f(u) to satisfy any convex, monotonic conditions and the regularity assumption we imposed on f(u) is weaker. 相似文献
3.
Yaojun Ye 《Mathematical Methods in the Applied Sciences》2017,40(12):4613-4624
In this paper, we prove the existence and uniqueness for the global solutions of Cauchy problem for coupled nonlinear Schrödinger equations and obtain the continuous dependence result on the initial data and the stronger decay estimate of global solutions. In particular, we show the existence and uniqueness of self‐similar solutions. Also, we build some asymptotically self‐similar solutions. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
4.
Chang‐Hua Wei 《Mathematical Methods in the Applied Sciences》2016,39(15):4563-4583
This paper investigates the smooth solution of 2D Chaplygin gas equations on an asymptotically flat Riemannian manifold. Under the assumption that the initial data are close to a constant state and the vorticity of the initial velocity vanishes, we prove the global existence of smooth solutions to the Cauchy problem for two‐dimensional flow of Chaplygin gases on curved space. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
5.
Luis J. Alías Marcos Dajczer Jaime Ripoll 《Annals of Global Analysis and Geometry》2007,31(4):363-373
The classical Bernstein theorem asserts that any complete minimal surface in Euclidean space
that can be written as the graph of a function on
must be a plane. In this paper, we extend Bernstein’s result to complete minimal surfaces in (may be non-complete) ambient
spaces of non-negative Ricci curvature carrying a Killing field. This is done under the assumption that the sign of the angle
function between a global Gauss map and the Killing field remains unchanged along the surface. In fact, our main result only
requires the presence of a homothetic Killing field.
L.J. Alías was partially supported by MEC/FEDER project MTM2004-04934-C04-02, F. Séneca project 00625/PI/04, and F. Séneca
grant 01798/EE/05, Spain 相似文献
6.
In this paper we study the asymptotic behavior of solutions of a first-order stochastic lattice dynamical system with a multiplicative noise.We do not assume any Lipschitz condition on the nonlinear term, just a continuity assumption together with growth and dissipative conditions, so that uniqueness of the Cauchy problem fails to be true.Using the theory of multi-valued random dynamical systems we prove the existence of a random compact global attractor. 相似文献
7.
In this paper, we prove the blow-up phenomena of smooth solutions to the Cauchy problem for the full compressible magnetohydrodynamic equations and isentropic compressible magnetohydrodynamic equations with constant and degenerate viscosities under some restrictions on the initial data. In particular, our results do not require that the initial data have compact support or contain vacuum in any finite region. 相似文献
8.
A. Alexandrou Himonas Gerard Misiolek A. Alexandrou Himonas Gerard Misiolek 《偏微分方程通讯》2013,38(1-2):123-139
We prove existence and uniqueness of local and global solutions of the periodic Cauchy problem for a higher order shallow water type equation under low regularity initial data. Using Fourier analysis we first prove local estimates in appropriate spaces and then use a contraction mapping argument and a conserved norm to get global existence. 相似文献
9.
本文证明了一类半线性波动方程组Cauchy问题整体解的存在唯一性.特别地,证明了自相似解的存在唯一性.同时还得到了渐近自相似解. 相似文献
10.
Ling Hsiao Qiangchang Ju Shu Wang 《Mathematical Methods in the Applied Sciences》2003,26(14):1187-1210
We establish the global existence of smooth solutions to the Cauchy problem for the multi‐dimensional hydrodynamic model for semiconductors, provided that the initial data are perturbations of a given stationary solutions, and prove that the resulting evolutionary solution converges asymptotically in time to the stationary solution exponentially fast. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
11.
Marc Herzlich 《Annales Henri Poincare》2016,17(12):3605-3617
We prove in a simple and coordinate-free way the equivalence between the classical definitions of the mass or of the center of mass of an asymptotically flat manifold and their alternative definitions depending on the Ricci tensor and conformal Killing fields. This enables us to prove an analogous statement in the asymptotically hyperbolic case. 相似文献
12.
L. F. Shampine 《Numerische Mathematik》1984,45(2):201-206
Summary Bulirsch and Stoer have shown how to construct asymptotic upper and lower bounds on the true (global) errors resulting from the solution by extrapolation of the initial value problem for a system of ordinary differential equations. It is shown here how to do this for any one-step method endowed with an asymptotically correct local error estimator. The one-step method can be changed at every step.This work performed at Sandia National Laboratories supported by the U.S. Department of Energy under contract number DE-AC04-76DP00789 相似文献
13.
Haruya Mizutani 《偏微分方程通讯》2013,38(2):169-224
The present article is concerned with Schrödinger equations on non-compact Riemannian manifolds with asymptotically conic ends. It is shown that, for any admissible pair (including the endpoint), local in time Strichartz estimates outside a large compact set are centered at origin hold. Moreover, we prove global in space Strichartz estimates under the nontrapping condition on the metric. 相似文献
14.
On a Riemannian manifold, a solution of the Killing equation is an infinitesimal isometry. Since the Killing equation is overdetermined, infinitesimal isometries do not exist in general. A completely determined prolongation of the Killing equation is a PDE on the bundle of 1-jets of vector fields. Restricted to a curve, this becomes an ODE that generalizes the Jacobi equation. A solution of this ODE is called an infinitesimal isometry along the curve, which we show to be an infinitesimal rigid variation of the curve. We define Killing transport to be the associated linear isometry between fibers of the bundle along the curve, and show that it is parallel translation for a connection on the bundle related to the Riemannian connection. Restricting to dimension two, we study the holonomy of this connection, prove the Gauss–Bonnet theorem by means of Killing transport, and determine the criteria for local existence of infinitesimal isometries. 相似文献
15.
This paper is devoted to study the Cauchy problem for certain incompressible magnetohydrodynamics‐α model. In the Sobolev space with fractional index s>1, we proved the local solutions for any initial data, and global solutions for small initial data. Furthermore, we also prove that as α→0, the MHD‐α model reduces to the MHD equations, and the solutions of the MHD‐α model converge to a pair of solutions for the MHD equations. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
16.
Ag. Kh. Khanmamedov 《Differential Equations》2010,46(3):461-462
We consider the Cauchy problem for the semi-infinite Volterra lattice with an asymptotically 2-periodic initial condition. We prove the global solvability of the problem in some class. 相似文献
17.
This paper studies the long time behavior of the following Cauchy problem The authors prove the existence of global attractor by showing the corresponding operator semigroup is asymptotically compact. 相似文献
18.
In this paper, we prove finite‐time blowup in energy space for the three‐dimensional Klein‐Gordon‐Zakharov (KGZ) system by modified concavity method. We obtain the blow‐up rates of solutions in local and global space, respectively. In addition, by using the energy convergence, we study the subsonic limit of the Cauchy problem for KGZ system and prove that any finite energy solution converges to the corresponding solution of Klein‐Gordon equation in energy space. 相似文献
19.
THEUNIQUENESSANDCONTINUOUSDEPENDENCEFORCHARACTERISTICCAUCHYPROBLEMOFPARTIALDIFFERENTIALEQUATIONSLuanWengui(栾文贵)(ComputingCent... 相似文献
20.
In this paper we prove infinite dimensionality of some local and global cohomology groups on abstract Cauchy–Riemann manifolds. 相似文献