共查询到20条相似文献,搜索用时 31 毫秒
1.
ZHANG Chao ZHOU Shulin 《偏微分方程(英文版)》2009,22(4):376-392
In this paper we establish the existence, uniqueness and long-time behavior of weak solutions for the initial-boundary value problem of a fourth-order degenerate parabolic equation with variable exponent of nonlinearity. 相似文献
2.
Fan Lili Yin Hui Zhao Huijiang 《偏微分方程(英文版)》2008,21(2):141-172
Abstract This paper is concerned with the initial-boundary value problem for damped wave equations with a nonlinear convection term in the half space R+{utt-txx+ut+f(u)x=0,t〉0,x∈R+,u(0,x)=u0(x)→u+,asx→+∞,ut(0,x)=u1(x),u(t,0)=ub.For the non-degenerate case f](u+) 〈 0, it is shown in [1] that the above initialboundary value problem admits a unique global solution u(t,x) which converges to the stationary wave φ(x) uniformly in x ∈ R+ as time tends to infinity provided that the initial perturbation and/or the strength of the stationary wave are sufficiently small. Moreover, by using the space-time weighted energy method initiated by Kawashima and Matsumura [2], the convergence rates (including the algebraic convergence rate and the exponential convergence rate) of u(t, x) toward φ(x) are also obtained in [1]. We note, however, that the analysis in [1] relies heavily on the assumption that f'(ub) 〈 0. The main purpose of this paper is devoted to discussing the case of f'(ub)= 0 and we show that similar results still hold for such a case. Our analysis is based on some delicate energy estimates. 相似文献
3.
In this paper, we introduce a new class of p-valent analytic functions defined by using a linear operator Lαk. For functions in this class Hαk(p, λ; h) we estimate the coefficients.Furthermore, some subordination properties related to the operator Lαkare also derived. 相似文献
4.
WANG Jinhuan TIAN Miaoqing HONG Liang 《偏微分方程(英文版)》2009,22(1):11-31
This paper studies a nonlinear diffusion system with coupled nonlinear boundary flux and two kinds of inner sources (positive for the first and negative for the second), where the four nonlinear mechanisms are described by eight nonlinear parameters. The critical exponent of the system is determined by a complete classification of the eight nonlinear parameters, which is represented via the characteristic algebraic system introduced to the problem. 相似文献
5.
This work deals with the numerical localization of small electromagnetic inhomogeneities. The underlying inverse problem considers, in a three-dimensional bounded domain, the time-harmonic Maxwell equations formulated in electric field. Typically, the domain contains a finite number of unknown inhomogeneities of small volume and the inverse problem attempts to localize these inhomogeneities from a finite number of boundary measurements. Our localization approach is based on a recent framework that uses an asymptotic expansion for the perturbations in the tangential boundary trace of the curl of the electric field. We present three numerical localization procedures resulting from the combination of this asymptotic expansion with each of the following inversion algorithms: the Current Projection method, the MUltiple Signal Classification (MUSIC) algorithm, and an Inverse Fourier method. We perform a numerical study of the asymptotic expansion and compare the numerical results obtained from the three localization procedures in different settings. 相似文献
6.
LI Junfeng LIU Weian 《偏微分方程(英文版)》2009,(3):266-281
This paper is concerned with the asymptotic behavior of solution to the following model involving two species all with chemotaxis:{αp/αt=Dp△(p△lnp/w),αp/αt=Dq△(q△lnq/w),αw/αt=βp-δw,p△ln(p/w).^-n=q△ln(q/w).^-n=0.We prove that the solution exists globally asβ ≥ 0. Asβ 〈 0, whether the solution exists globally or not depends on the initial data. By function transformation and compari- son, the asymptotical behavior of the solution is studied. 相似文献
7.
WU Haigen 《偏微分方程(英文版)》2009,22(1):74-96
In this paper we consider the Cauchy problem for a semi-linear system of wave equations with Hamilton structure. We prove the existence of global smooth solution of the system for subcritical case by using conservation of energy and Strichartz's estimate. On the basis of Morawetz-Pohozev identity, we obtain the same result for the critical case. 相似文献
8.
Zagharide Zine EL ABIDINE 《数学物理学报(B辑英文版)》2014,(5):1404-1416
Let m be a positive integer and B be the unit ball of Rn(n ≥ 2). We investigate the existence, uniqueness and the asymptotic behavior of a positive continuous solution to the following semilinear polyharmonic boundary value problem(-△)mu = a1(x)uα1+ a2(x)uα2, lim|x|→1u(x)(1- |x|)m-1= 0,where α1, α2 ∈(-1, 1) and a1, a2 are two nonnegative measurable functions on B satisfying some appropriate assumptions related to Karamata regular variation theory. 相似文献
9.
Cemil Tun 《Annals of Differential Equations》2014,(3):253-257
In this paper, we consider a class of nonlinear vector differential equations of sixth order. By constructing appropriate Lyapunov functions, the non-existence of periodic solutions is established. Moreover, we provide an example to show the feasibility of our results. Our results extend and improve two related results in the previous literature from scalar cases to vectorial cases. 相似文献
10.
This paper discuses three types of phase synchronization phenomena in extended Kuramoto model. A certain quadratic form is applied to analyze the stability of phase synchronization manifolds without any stability knowledge for error systems. Some simple and convenient criteria are obtained for these types of phase synchronization. Also, the effectiveness of the proposed criteria is illustrated successfully by an example. 相似文献
11.
This paper presents and analyzes a monotone domain decomposition algorithm for solving nonlinear singularly perturbed reaction-diffusion problems of parabolic type. To solve the nonlinear weighted average finite difference scheme for the partial differential equation, we construct a monotone domain decomposition algorithm based on a Schwarz alternating method and a box-domain decomposition. This algorithm needs only to solve linear discrete systems at each iterative step and converges monotonically to the exact solution of the nonlinear discrete problem. domain decomposition algorithm is estimated The rate of convergence of the monotone Numerical experiments are presented. 相似文献
12.
In this paper, we axe interested in the existence of three positive solutions to a BVP for p-Laplacian impulsive functional dynamic equations on a time scale. Using the five-functional fixed theory, we establish a Banach space and an appropriate operator. In this paper, we combine the delta-nabla p-Laplacian BVP with impulsive functional dynamic equations, and obtain some new sufficient conditions for the existence of three positive solutions to the BVP, and our result here generalizes the previous related results. 相似文献
13.
Yuan Jia 《偏微分方程(英文版)》2008,21(3):208-220
We give blow-up criteria of strong solutions of Navier-Stokes equations with its initial data in Besov spaces and consider the regularity of Leray-Hopf solutions of the equation. 相似文献
14.
Ruan Lizhi Zhu Changjiang 《偏微分方程(英文版)》2008,21(2):173-192
We consider the asymptotic behavior of solutions to a model of hyperbolicelliptic coupled system on the half-line R+ = (0, ∞),with the Dirichlet boundary condition u(0, t) = 0. S. Kawashima and Y. Tanaka [Kyushu J. Math., 58(2004), 211-250] have shown that the solution to the corresponding Cauchy problem behaviors like rarefaction waves and obtained its convergence rate when u_ u+. Our main concern in this paper is the boundary effect. In the case of null-Dirichlet boundary condition on u, asymptotic behavior of the solution (u, q) is proved to be rarefaction wave as t tends to infinity. Its convergence rate is also obtained by the standard L2-energy method and Ll-estimate. It decays much lower than that of the corresponding Cauchy problem. 相似文献
15.
Dan Li Yansheng He Chengmin Hou 《Annals of Differential Equations》2014,(3):301-311
By establishing the corresponding variational framework, and using critical point theory, we give the existence of multiple solutions to a fractional difference boundary value problem with parameter. Under some suitable assumptions we obtain some results which ensure the existence of well precise interval of parameter for which the problem admits multiple solutions. 相似文献
16.
Xiaogang Liu 《Annals of Differential Equations》2014,(2):157-165
A class of nonlinear fractional order differential equations with delay is investigated in this paper. Using Leray-Schauder fixed point theorem and the contraction mapping theorem, we obtain some sufficient conditions for the existence and uniqueness of solutions to the fractional order differential equations. 相似文献
17.
A monotone compact implicit finite difference scheme with fourth-order accuracy in space and second-order in time is proposed for solving nonlinear reaction-diffusion equations. An accelerated monotone iterative method for the resulting discrete problem is presented. The sequence of iteration converges monotonically to the unique solution of the discrete problem, and the convergence rate is either quadratic or nearly quadratic, depending on the property of the nonlinear reaction. The numerical results illustrate the high accuracy of the proposed scheme and the rapid convergence rate of.the iteration. 相似文献
18.
Cui Dacheng Yin Huicheng 《偏微分方程(英文版)》2008,21(3):263-288
In this paper, by use of the methods in [1-3], we establish the uniqueness of a 2-D transonic shock solution in a nozzle when the end pressure in the diverging part of the nozzle lies in an appropriate scope. Especially, we remove the crucial but unnatural assumption in recent references which the transonic shock must be assumed to go through a fixed point in advance. 相似文献
19.
In this paper, we consider a generalized model of the two friction models, both of which have two different types of control forces with time-delayed feedback proposed by Ashesh Sara et al. By taking the time delay as the bifurcation parameter, we discuss the local stability of the Hopf bifurcations. Under some condition, the generalized model harbors a phenomenon that the equilibrium may undergo finite switches from stability to instability to stability and finally become unstable. By applying the method introduced by Faria and Magalhaes, we compute the normal form on the center manifold to determine the direction and stability of the Hopf bifurcations. Numerical simulations are carried out and more than one periodic solutions may exist according to the bifurcation diagram given by BIFTOOL. Finally a brief conclusion is presented. 相似文献
20.
In this paper, local a priori, local a posteriori and global a posteriori error estimates are obtained for TQC9 element for the biharmonic equation. An adaptive algorithm is given based on the a posteriori error estimates. 相似文献