共查询到20条相似文献,搜索用时 437 毫秒
1.
求解非线性方程组的一种新的全局收敛的Levenberg-Marquardt算法 总被引:10,自引:0,他引:10
本文提出了求解非线性方程组的一种新的全局收敛的Levenberg-Marquardt算法,即μk=ακ(θ||F_k|| (1-θ)||J_k~TF_k||),θ∈[0,1],其中ακ利用信赖域技巧来修正.在不必假设雅可比矩阵非奇异的局部误差界条件下,证明了该算法是全局收敛和局部二次收敛的.数值试验表明该算法能有效地求解奇异非线性方程组问题. 相似文献
2.
A NECESSARY AND SUFFICIENT CONDITION OF EXISTENCE OF GLOBAL SOLUTIONS FOR SOME NONLINEAR HYPERBOLIC EQUATIONS 总被引:2,自引:0,他引:2
Zhang Quande 《数学年刊B辑(英文版)》1995,16(4):461-468
ANECESSARYANDSUFFICIENTCONDITIONOFEXISTENCEOFGLOBALSOLUTIONSFORSOMENONLINEARHYPERBOLICEQUATIONS¥ZHANGQUANDE(DepartmentofMathe... 相似文献
3.
In this paper we prove, under various conditions, the so-called Lojasiewicz inequality
$ \| E' (u + \varphi) \| \geq \gamma|E(u+\varphi) - E(\varphi)|^{1-\theta} $, where
$ \theta \in (0,1/2] $, and > 0, while $ \| u \| $ is sufciently small and is a
critical point of the energy functional E supposed to be only
C⊃, instead of analytic in the classical settings. Here
E can be for instance the energy associated to the semilinear heat
equation $u_t = \Delta u - f(x,u) $ on a bounded domain $ \Omega \subset \mathbb{R}^N $.
As a corollary of this inequality we give the rate of convergence of the solution
u(t) to an equilibrium, and we exhibit examples showing that the
given rate of convergence (which depends on the exponent and on the critical
point through the nature of the kernel of the linear operator $ E' (\varphi)) $ is optimal. 相似文献
4.
Kenji Nishihara 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2006,41(6):604-614
We consider the Cauchy problem for the nonlinear dissipative evolution system with ellipticity on one dimensional space
$ \left\{{{ll} {\psi_t=-\left({1-\alpha}\right)\psi-\theta_x+\alpha\psi_{xx},}&{\left( {t,x} \right) \in \left( {0,\infty } \right) \times {\bf R}}\\ {\theta _t = - \left( {1 - \alpha } \right)\theta + \nu ^2 \psi _x + \alpha \theta _{xx} + 2\psi \theta _x ,} } \right. $ \left\{{\begin{array}{ll} {\psi_t=-\left({1-\alpha}\right)\psi-\theta_x+\alpha\psi_{xx},}&{\left( {t,x} \right) \in \left( {0,\infty } \right) \times {\bf R}}\\ {\theta _t = - \left( {1 - \alpha } \right)\theta + \nu ^2 \psi _x + \alpha \theta _{xx} + 2\psi \theta _x ,} \end{array}} \right. 相似文献
5.
We establish new Kamenev-type oscillation criteria for the half-linear partial differential equation with damping under quite general conditions. These results are extensions of the recent results developed by Sun [Y.G. Sun, New Kamenev-type oscillation criteria of second order nonlinear differential equations with damping, J. Math. Anal. Appl. 291 (2004) 341-351] for second order ordinary differential equations in a natural way, and improve some existing results in the literature. As applications, we illustrate our main results using two different types of half-linear partial differential equations. 相似文献
6.
In this paper, we consider the stochastic heat equation of the form $$\frac{\partial u}{\partial t}=(\Delta_\alpha+\Delta_\beta)u+\frac{\partial f}{\partial x}(t,x,u)+\frac{\partial^2W}{\partial t\partial x},$$ where $1<\beta<\alpha< 2$, $W(t,x)$ is a fractional Brownian sheet, $\Delta_\theta:=-(-\Delta)^{\theta/2}$ denotes the fractional Lapalacian operator and $f:[0,T]\times \mathbb{R}\times \mathbb{R}\rightarrow\mathbb{R}$ is a nonlinear measurable function. We introduce the existence, uniqueness and H\"older regularity of the solution. As a related question, we consider also a large deviation principle associated with the above equation with a small perturbation via an equivalence relationship between Laplace principle and large deviation principle. 相似文献
7.
Da-Xue Chen 《Acta Appl Math》2010,109(3):703-719
In this paper, we derive some sufficient conditions for the oscillation and asymptotic behavior of the nth-order nonlinear neutral delay dynamic equations
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