共查询到20条相似文献,搜索用时 15 毫秒
1.
Diethelm Kai Kitzing Konrad Picard Rainer Siegmund Stefan Trostorff Sascha Waurick Marcus 《Journal of Dynamics and Differential Equations》2022,34(1):481-504
Journal of Dynamics and Differential Equations - We study fractional differential equations of Riemann–Liouville and Caputo type in Hilbert spaces. Using exponentially weighted spaces of... 相似文献
2.
Anke Kalauch Rainer Picard Stefan Siegmund Sascha Trostorff Marcus Waurick 《Journal of Dynamics and Differential Equations》2014,26(2):369-399
We discuss ordinary differential equations with delay and memory terms in Hilbert spaces. By introducing a time derivative as a normal operator in an appropriate Hilbert space, we develop a new approach to a solution theory covering integro-differential equations, neutral differential equations and general delay differential equations within a unified framework. We show that reasonable differential equations lead to causal solution operators. 相似文献
3.
Damião Araújo Eduardo V. Teixeira 《Archive for Rational Mechanics and Analysis》2013,209(3):1019-1054
In this work we develop a systematic geometric approach to study fully nonlinear elliptic equations with singular absorption terms, as well as their related free boundary problems. The magnitude of the singularity is measured by a negative parameter (γ - 1), for 0 < γ < 1, which reflects on lack of smoothness for an existing solution along the singular interface between its positive and zero phases.We establish existence as well as sharp regularity properties of solutions. We further prove that minimal solutions are non-degenerate and we obtain fine geometric-measure properties of the free boundary ${\mathfrak{F} = \partial{u > 0}}$ . In particular, we show sharp Hausdorff estimates which imply local finiteness of the perimeter of the region {u > 0} and the ${\mathcal{H}^{n-1}}$ almost-everywhere weak differentiability property of ${\mathfrak{F}}$ . 相似文献
4.
John M. Seiner 《Theoretical and Computational Fluid Dynamics》1998,10(1-4):373-383
This paper offers a new rational approach to jet noise suppression methodology. The tools required to implement such an approach
are discussed. These involve the use of global velocimetry to measure those Lighthill turbulent stress tensor terms thought
most important to noise generation. The framework of the dynamic systems model as it applies to the development of a noise
suppression model is discussed, as well as the latest results on the development of an actuator for control input. The dynamic
systems model offers a unique opportunity to study the influence of a concept noise reduction scheme on noise reduction through
appropriate algorithms that relate turbulent jet processes to noise.
Received 24 January 1997 and accepted 30 May 1997 相似文献
5.
Alessandro Calamai Cristina Marcelli Francesca Papalini 《Journal of Dynamics and Differential Equations》2009,21(4):567-593
We investigate the persistence of front propagation for functional reaction-diffusion equations
_boxclose_boxclose = v_xx + F(v)v_\tau = v_{xx} + F(v) 相似文献
6.
Cristina Pignotti 《Journal of Dynamics and Differential Equations》2017,29(4):1309-1324
It is well-known that wave-type equations with memory, under appropriate assumptions on the memory kernel, are uniformly exponentially stable. On the other hand, time delay effects may destroy this behavior. Here, we consider the stabilization problem for second-order evolution equations with memory and intermittent delay feedback. We show that, under suitable assumptions involving the delay feedback coefficient and the memory kernel, asymptotic or exponential stability are still preserved. In particular, asymptotic stability is guaranteed if the delay feedback coefficient belongs to \(L^1(0, +{\infty })\) and the time intervals where the delay feedback is off are sufficiently large. 相似文献
7.
8.
We show that one can apply a Lagrangian approach to certain evolution equations by considering them together with their associated equations. Consequently, one can employ Noether's theorem and derive conservation laws from symmetries of coupled systems of evolution equations. We discuss in detail the linear and non-linear heat equations as well as the Burgers equation and obtain new non-local conservation laws for the non-linear heat and the Burgers equations by extending their symmetries to the associated equations. We also provide Lagrangians for non-linear Schrödinger and Korteweg—de Vries type systems. 相似文献
9.
10.
Guy Barles Samuel Biton Olivier Ley 《Archive for Rational Mechanics and Analysis》2002,162(4):287-325
In this article, we are interested in the existence and uniqueness of solutions for quasilinear parabolic equations set in the whole space ? N . We consider, in particular, cases when there is no restriction on the growth or the behavior of these solutions at infinity. Our model equation is the mean-curvature equation for graphs for which Ecker and Huisken have shown the existence of smooth solutions for any locally Lipschitz continuous initial data. We use a geometrical approach which consists in seeing the evolution of the graph of a solution as a geometric motion which is then studied by the so-called “level-set approach”. After determining the right class of quasilinear parabolic PDEs which can be taken into account by this approach, we show how the uniqueness for the original PDE is related to “fattening phenomena” in the level-set approach. Existence of solutions is proved using a local L ∞ bound obtained by using in an essential way the level-set approach. Finally we apply these results to convex initial data and prove existence and comparison results in full generality, i.e., without restriction on their growth at infinity. 相似文献
11.
Sigrun I. Bodine Robert J. Sacker 《Journal of Dynamics and Differential Equations》2000,12(1):229-245
We study the asymptotic diagonalization of a system consisting of an
-matrix plus a finite number of
-perturbations on an interval I
0=[t
0, ), where p, m
i[1, ). Using linear skew-product flows and spectral theory, we show that if the unperturbed system has full spectrum over its omega-limit set, then the entire system is asymptotically diagonalizable almost everywhere. 相似文献
12.
We introduce a new class of non-isothermal models describing the evolution of nematic liquid crystals and prove their consistency with the fundamental laws of classical thermodynamics. The resulting system of equations captures all essential features of physically relevant models; in particular, the effect of stretching of the director field is taken into account. In addition, the associated initial-boundary value problem admits global-in-time weak solutions without any essential restrictions on the size of the initial data. 相似文献
13.
Philippe G. Ciarlet Liliana Gratie Cristinel Mardare 《Archive for Rational Mechanics and Analysis》2008,188(3):457-473
The fundamental theorem of surface theory classically asserts that, if a field of positive-definite symmetric matrices (a
αβ
) of order two and a field of symmetric matrices (b
αβ
) of order two together satisfy the Gauss and Codazzi-Mainardi equations in a simply connected open subset ω of , then there exists an immersion such that these fields are the first and second fundamental forms of the surface , and this surface is unique up to proper isometries in . The main purpose of this paper is to identify new compatibility conditions, expressed again in terms of the functions a
αβ
and b
αβ
, that likewise lead to a similar existence and uniqueness theorem. These conditions take the form of the matrix equation
14.
A Predictor-Corrector Approach for the Numerical Solution of Fractional Differential Equations 总被引:4,自引:0,他引:4
We discuss an Adams-type predictor-corrector method for the numericalsolution of fractional differential equations. The method may be usedboth for linear and for nonlinear problems, and it may be extended tomulti-term equations (involving more than one differential operator)too. 相似文献
15.
Existence of weak solutions to the 3-D semi-geostrophic equations with rigid boundaries was proved by Benamou and Brenier
[3], using Monge transport theory. This paper extends the results to a free surface boundary condition, which is more physically
appropriate. This extension is at present for the 2-D shallow water case only. In addition, we establish stronger time regularity
than was possible in [3].
Accepted October 9, 2000?Published online February 14, 2001 相似文献
16.
含模糊参数结构有限元方程的一种新解法 总被引:3,自引:0,他引:3
实际工程问题中,常常会包含一些难以准确描述的系统参数。本文根据模糊集理论,将结构中的不确定参数转化为模糊参数,从而建立起含模糊参数的有限元平衡方程,应用一般模糊线性方程解的基本原理,对模糊有限元平衡方程解的概念及方法进行了讨论,并在此基础上提出了一种改进解的概念以及以摄动法为基础的求解方法。该方法假定当不确定参数相对于其清晰值的分解度不很大时,可以将其在清晰值附近作摄动展开。文中也简要讨论了改进解与现有的模糊有限元方程组各种解之间的关系。相对于现有的其它解法,本文建议的方法更易于与常规的有限元软件结合,用于处理工程实际问题。对算例结果的分析表明,本文方法可较好地符合实际要求。 相似文献
17.
Guy Barles Panagiotis E. Souganidis 《Archive for Rational Mechanics and Analysis》1998,141(3):237-296
In this paper we present a new definition for the global in time propagation (motion) of fronts (hypersurfaces, boundaries)
with a prescribed normal velocity, past the first time they develop singularities. We show that if this propagation satisfies
a geometric maximum principle (inclusion‐avoidance)‐type property, then the normal velocity must depend only on the position
of the front and its normal direction and principal curvatures. This new approach, which is more geometric and, as it turns
out, equivalent to the level‐set method, is then used to develop a very general and simple method to rigorously validate the
appearance of moving interfaces at the asymptotic limit of general evolving systems like interacting particles and reaction‐diffusion
equations. We finally present a number of new asymptotic results. Among them are the asymptotics of (i) reaction‐diffusion
equations with rapidly oscillating coefficients, (ii) fully nonlinear nonlocal (integral differential) equations and (iii)
stochastic Ising models with long-range anisotropic interactions and general spin flip dynamics.
(Accepted July 8, 1996) 相似文献
18.
Extraction of quantitative features from observations via suitable measuring devices M means that the words of science are coded as numbers, and the syntaxis is a set of mathematical rules. Once general premises are available all consequences can be worked in a purely deductive way. This characteristic of science displays two orders of drawbacks, namely, undecidability of deductive procedures, and intractability of computer modelings of complex situations. The way out of such a crisis consists in an adaptive strategy, that is, in a frequent readjustment of M suggested by the observed events. As a consequence, M provides different data streams (words) for the same observed events, as it is tuned to different resolutions. The adaptive strategy here introduced should by no means be confused with the adaptivity of a learning machine, which—inputted by a data stream—readjusts itself over a class of theoretical explanations in order to select the optimal one, thus providing knowledge conditional on the assigned input. On the contrary, physics aims at extracting regular patterns out of things, by a trial and error procedure which includes not only modifications of the explanations for fixed data sets, but also exploring different data sets via modified M's. This M-adjustment is a pre-linguistic endeavour, not expressible by a formal language. Such an essential characteristic of the physical program means that physics can not be performed by a machine. 相似文献
19.
Keith Julien Edgar Knobloch Joseph Werne 《Theoretical and Computational Fluid Dynamics》1998,11(3-4):251-261
The incompressible Navier–Stokes equation is considered in the limit of rapid rotation (small Ekman number). The analysis
is limited to horizontal scales small enough so that both horizontal and vertical velocities are comparable, but the horizontal
velocity components are still in geostrophic balance. Asymptotic analysis leads to a pair of nonlinear equations for the vertical
velocity and vertical vorticity coupled by vertical stretching. Statistically stationary states are maintained against viscous
dissipation by boundary forcing or energy injection at larger scales. For thermal forcing direct numerical simulation of the
reduced equations reveals the presence of intense vortical structures spanning the layer depth, in excellent agreement with
simulations of the Boussinesq equations for rotating convection by Julien et al. (1996).
Received 30 May 1997 and accepted 4 January 1998 相似文献
20.
一种求解柔性多体系统动力学方程的新方法 总被引:1,自引:0,他引:1
柔性多体系统控制方程是具有stiff性质的刚柔耦合非线性代数一微分方程组,本文提出了一种求解该类刚性方程组的数值方法,在每一时间步,利用Newmark-β直接积分法计算迭代初值,基于控制方程及约束方程的泰勒展开,推导出Newton-Raphson迭代公式,对位移及拉格朗日乘子进行修正,最后,引用Blajer提出的违约修正方法对数值积分过程中约束方程的违约进行修正。就两个典型算例进行了数值仿真,结果证明了本文方法的有效性。 相似文献
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