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Theoretical and applied fracture mechanics (Print), 2018
A novel method of the time-dependent reliability, which combines the perturbation series expansions with the interval mathematics, is presented in this study for life prediction of fatigue crack growth problems. Distinct from the treatment in statistical
Lei Wang +3 more
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A novel method of the time-dependent reliability, which combines the perturbation series expansions with the interval mathematics, is presented in this study for life prediction of fatigue crack growth problems. Distinct from the treatment in statistical
Lei Wang +3 more
semanticscholar +1 more source
Maximum principle via singular perturbations
Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304), 2003The paper is concerned with necessary optimality conditions for parabolic boundary control problems. Its main purpose is to provide a regularization technique via singular perturbations to obtain optimality conditions for the time optimal control problem. The considered system is nonlinear and consists of a controlled coupled ODE/PDE.
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On the integrability and perturbations of systems of Ode's with nonlinear superposition principles
Physica D: Nonlinear Phenomena, 1986In this note - properly characterized as ''extended abstract'' by the authors themselves - the authors announce that they are currently investigating a variety of manifestations of chaotic behavior in different perturbations of systems of ODE's with nonlinear superposition principles.
Bountis, T. C. +2 more
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Maximum Principle for a Hybrid System Via Singular Perturbations
SIAM Journal on Control and Optimization, 1999This paper is on a boundary control problem for a linear parabolic equation coupled with an infinite dimensional ordinary differential equation. As the author points out, to obtain a Pontryagin maximum principle in the presence of pointwise state constraints, one needs an adjoint variational equation with measure boundary data.
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Non-uniqueness and h-Principle for Hölder-Continuous Weak Solutions of the Euler Equations
, 2016In this paper we address the Cauchy problem for the incompressible Euler equations in the periodic setting. We prove that the set of Hölder $${1/5 - \varepsilon}$$1/5-ε wild initial data is dense in $${L^{2}}$$L2, where we call an initial datum wild if ...
S. Daneri, L. Székelyhidi
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On Reduction Principle in Stability Theory for Systems with Random Perturbations
Ukrainian Mathematical Journal, 2001The author considers a system of the form \[ \dot x=X(x,y),\quad \dot y=A(t)y+Y(t,x,y,\xi(t)),\tag{1} \] where \(X\in C(D_x\times D_y \mapsto \mathbb{R}^n)\), \(Y\in C([0,\infty)\times D_x\times D_y\times \mathbb{R}^k \mapsto \mathbb{R}^m)\), \(D_x\), \(D_y\) are domains in \(\mathbb{R}^n\) and \(\mathbb{R}^m\), respectively, and \(\xi(t)\) is an ...
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The Samoilenko Reduction Principle for Differential Equations with Random Perturbations
Differential Equations, 2001Let \(x(t,t_0,x_0)\) be a solution to the randomly perturbed differential equation \[ dx/dt=F(x) +\sigma(t,x)\xi(f),\quad t\geq 0,\tag{*} \] with \(x\in \mathbb{R}^n\), \(\xi(t)\) a random process a.s. absolutely integrable on every finite interval, and \(F,\sigma \in\text{Lip}\). The set \(S_t\) is said to be positively invariant if \[ P\{x(t,t_0,x_0)\
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Genericity of Well-Posedness, Perturbations and Smooth Variational Principles
Set-Valued Analysis, 2001The author introduces the notions of flexible and tolerant perturbation functions and shows that for a flexible and tolerant perturbation function the set of parameters for which the corresponding minimization problem is well-posed is generic. Then he gives criteria for flexible (resp.\ tolerant) perturbations, obtaining so several genericity results ...
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