共查询到20条相似文献,搜索用时 81 毫秒
1.
Karen Yagdjian 《偏微分方程通讯》2013,38(3):447-478
In this article we study global in time (not necessarily small) solutions of the equation for the Higgs boson in the Minkowski and in the de Sitter spacetimes. We reveal some qualitative behavior of the global solutions. In particular, we formulate sufficient conditions for the existence of the zeros of global solutions in the interior of their supports, and, consequently, for the creation of the so-called bubbles, which have been studied in particle physics and inflationary cosmology. We also give some sufficient conditions for the global solution to be oscillatory in time. 相似文献
2.
Nakao Hayashi 《偏微分方程通讯》2013,38(7-8):1109-1124
Abstract. We study the global existence of small solutions to some quadratic nonlinear Schrödinger equations in three or four space dimensions. 相似文献
3.
This paper is concerned with the initial value problem for semilinear systems of wave equations. First we show a global existence
result for small amplitude solutions to the systems. Then we study asymptotic behavior of the global solution. We underline
that ``modified' free profiles are obtained for all global solutions to the systems even in the case where the free profile
might not exist. Moreover, we prove non–existence of any free profiles for the global solution in some cases where the effect
of the nonlinearity is strong enough.
The first author was partially supported by Grant-in-Aid for Science Research (14740114), JSPS. 相似文献
4.
Soichiro Katayama 《Journal of Differential Equations》2005,209(1):140-171
We consider the Cauchy problem for systems of nonlinear wave equations with different propagation speeds in three space dimensions. We prove global existence of small amplitude solutions for systems with some nonresonant nonlinearities which may depend on both of the unknowns and their derivatives. Our method here can be also adopted to treat the null forms. 相似文献
5.
Jong Uhn Kim 《Journal of Differential Equations》2011,250(3):1650-1684
We establish the existence and uniqueness of a local smooth solution to the Cauchy problem for a quasi-linear symmetric hyperbolic system with random noise in Rd. When the noise is multiplicative satisfying some nondegenerate conditions and the initial data are sufficiently small, we show that the solution exists globally in time in probability, i.e., the probability of global existence can be made arbitrarily close to one if the initial date are small accordingly. 相似文献
6.
We consider Kirchhoff equations with strong damping, namely with a friction term which depends on a power of the “elastic” operator. We address local and global existence of solutions in two different regimes depending on the exponent in the friction term. When the exponent is greater than 1/2, the dissipation prevails, and we obtain global existence in the energy space, assuming only degenerate hyperbolicity and continuity of the nonlinear term. When the exponent is less than 1/2, we assume strict hyperbolicity and we consider a phase space depending on the continuity modulus of the nonlinear term and on the exponent in the damping. In this phase space, we prove local existence and global existence if initial data are small enough. The regularity we assume both on initial data and on the nonlinear term is weaker than in the classical results for Kirchhoff equations with standard damping. Proofs exploit some recent sharp results for the linearized equation and suitably defined interpolation spaces. 相似文献
7.
In this paper we consider the local and global well-posedness to the density-dependent incompressible viscoelastic fluids. We first study some linear models associated to the incompressible viscoelastic system. Then we approximate the system by a sequence of ordinary differential equations, by means of the Friedrichs method. Some uniform estimates for those solutions will be obtained. Using compactness arguments, we will get the local existence up to extracting a subsequence by means of Ascoli’s lemma. With the help of small data conditions and hybird Besov spaces, we finally derive the global existence. 相似文献
8.
对于α的某一取值范围,应用广义Strichartz不等式和压缩映射原理研究了初值在弱Lp空间中足够小的条件下,非线性Schr(o)dinger方程Cauchy问题整体解和自相似解的存在性. 相似文献
9.
Martin Väth 《Annali di Matematica Pura ed Applicata》2007,186(2):199-227
We show some abstract (purely set-topological) principles which allow to prove the existence of global solution branches.
The results apply either for the locally compact situation and then allow to prove global bifurcation results of Rabinowitz
type, or they apply for a locally connected situation and allow to prove global branches of arbitrarily small perturbations
without any compactness hypotheses. As two applications, we obtain a generalization of the Rabinowitz theorem for bifurcation
from an interval and an implicit function type theorem for nondifferentiable functions. 相似文献
10.
Global existence and asymptotic behavior of solution for Rosenau equation with Stokes damped term 下载免费PDF全文
We study the small‐data Cauchy problem for n‐dimensional Stokes damped Rosenau equation. Under some assumptions, we prove the global existence and uniqueness of the small‐amplitude solution by utilizing the contraction mapping principle and study the asymptotic behavior of the solution. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
11.
Shangbing Ai 《Journal of Differential Equations》2007,232(1):104-133
We study the existence of traveling wave fronts for a reaction-diffusion equation with spatio-temporal delays and small parameters. The equation reduces to a generalized Fisher equation if small parameters are zero. We present two results. In the first one, we deal with the equation with very general kernels and show the persistence of Fisher wave fronts for all sufficiently small parameters. In the second one, we deal with some particular kernels, with which the nonlocal equation can be reduced to a system of singularly perturbed ODEs, and we are then able to apply the geometric singular perturbation theory and phase plane arguments to this system to show the existence of the minimal wave speed, the existence of a continuum of wave fronts, and the global uniqueness of the physical wave front with each wave speed. 相似文献
12.
该文讨论了一类在量子理论中有着较多应用的具耗散项的非线性Hartree方程。分别从耗散系数和初值两个方面讨论了解的整体存在性条件。一方面,利用Strichartz估计,得到仅依赖于耗散系数的整体存在性条件。另一方面,也得到了仅依赖于初值大小的整体存在性条件。而且,还得到了一个整体解存在的小初值准则。 相似文献
13.
We consider the general nonlinear heat equation on where and g satisfies certain growth conditions. We prove the existence of global solutions for small initial data with respect to a
norm which is related to the structure of the equation. We also prove that some of those global solutions are asymptotic for
large time to self-similar solutions of the single power nonlinear heat equation, i.e. with
Received: 23 July 1999 / Accepted: 14 December 2000 / Published online: 23 July 2001 相似文献
14.
0IntroductionInthispaper,weconsidertheinitial-boundaryvalueproblemforthefailliliarequationwherefiisaboundeddomaininR"withsmoothboulldaryoff,p22isacollstantalldlp(z,u)l5of'(tl" 'forsomea20andc>0.FOrp(x,ti)=Itll"'u,theauthorsofpaper[4,7llolwereillterestedillllollllegativesolutionandhadobtainedfollowillgresults(alsosee[12]).1)If25a 2
相似文献
15.
Peng ZhouJie Bao Zhigui Lin 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(7):2523-2533
This paper is concerned with a double fronts free boundary problem for the heat equation with a localized nonlinear reaction term. The local existence and uniqueness of the solution are given by applying the contraction mapping theorem. Then we present some conditions so that the solution blows up in finite time. Finally, the long-time behavior of the global solution is discussed. We show that the solution is global and fast if the initial data is small and that a global slow solution is possible when the initial data is suitably large. 相似文献
16.
Matthew D. Blair Hart F. Smith Christopher D. Sogge 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2009,26(5):1817-1829
We prove certain mixed-norm Strichartz estimates on manifolds with boundary. Using them we are able to prove new results for the critical and subcritical wave equation in 4-dimensions with Dirichlet or Neumann boundary conditions. We obtain global existence in the subcritical case, as well as global existence for the critical equation with small data. We also can use our Strichartz estimates to prove scattering results for the critical wave equation with Dirichlet boundary conditions in 3-dimensions. 相似文献
17.
We study a type of nonlinear parabolic equations. In terms of the variational characterization of the corresponding nonlinear elliptic equations and the invariant flow arguments, we establish the sharp criteria for global existence and blow-up. Furthermore, we also get the instability of the steady states and the global existence with small initial data. 相似文献
18.
本文研究Dalvey-Stewartson方程组的整体解与自相似解的存在性.首先,运用Ba- nach不动点定理得到一个关于解整体存在性的一般性定理,然后把一类特殊的初始值用到该存在性结果上去从而得到自相似解存在的结论. 相似文献
19.
We study an energy conserving distributed parameter system described by a nonlinear string equation with the input and output at the boundary. We prove the existence of global smooth solutions to this quasilinear hyperbolic system if the initial data and the boundary input are small. If, moreover, the input function becomes zero after some finite time, then the state trajectories decay exponentially. 相似文献
20.
Dao Yuan FANG Ru Ying XUE 《数学学报(英文版)》2006,22(4):1085-1102
In this paper, we consider a system of two cubic quasi-linear Klein-Gordon equations with different masses for small, smooth, compactly supported Cauchy data in one space dimension. We show that such a system has global existence when the nonlinearities satisfy a convenient null condition. Our results extend the global existence proved by Sunagawa recently under the non-resonance assumption to that under the resonance assumption. 相似文献