Almost-Everywhere Stability of Systems with a Piecewise-C2 Lipschitz Continuous Vector Field

2011 ◽  
Vol 44 (1) ◽  
pp. 10928-10933
Author(s):  
Izumi Masubuchi
Keyword(s):  
Vector Field ◽  
Continuous Vector ◽  
Lipschitz Continuous ◽  
Almost Everywhere ◽  
Continuous Vector Field

scholarly journals Weak solutions of differential equations in Banach spaces

1986 ◽  
Vol 33 (3) ◽  
pp. 407-418 ◽  
Author(s):  
Nikolaos S. Papageorgiou
Keyword(s):  
Banach Space ◽  
Cauchy Problem ◽  
Vector Field ◽  
Banach Spaces ◽  
Existence Result ◽  
Measure Of Noncompactness ◽  
Continuous Vector ◽  
Weakly Continuous ◽  
Continuous Vector Field ◽  
The Cauchy Problem

We consider the Cauchy problem x (t) = f (t,x (t)), x (0) = x0 in a nonreflexive Banach space X and for f: T × X → X a weakly continuous vector field. Using a compactness hypothesis involving a weak measure of noncompactness we prove an existence result that generalizes earlier theorems by Chow-Shur, Kato and Cramer-Lakshmikantham-Mitchell.

scholarly journals Modelling white matter in gyral blades as a continuous vector field

NeuroImage ◽  
2020 ◽  
pp. 117693
Author(s):  
Michiel Cottaar ◽  
Matteo Bastiani ◽  
Nikhil Boddu ◽  
Matthew F. Glasser ◽  
Suzanne Haber ◽  
...  
Keyword(s):  
Vector Field ◽  
White Matter ◽  
Continuous Vector ◽  
Continuous Vector Field

Remarks on a semilinear system in ℝn motivated by difference equations

2018 ◽  
Vol 68 (5) ◽  
pp. 1075-1082
Author(s):  
Diogo Caetano ◽  
Luís Sanchez
Keyword(s):  
Vector Field ◽  
Difference Equations ◽  
Nonlinear Term ◽  
Linear Part ◽  
Continuous Vector ◽  
One Dimensional ◽  
Continuous Vector Field

Abstract We study some conditions of solvability of a semilinear system in ℝn, where the linear part is represented by an n × n matrix with one-dimensional kernel and the nonlinear term is a sublinear, continuous vector field.

scholarly journals On Rice's Formula for Stationary Multivariate Piecewise Smooth Processes

2012 ◽  
Vol 49 (2) ◽  
pp. 351-363 ◽  
Author(s):  
K. Borovkov ◽  
G. Last
Keyword(s):  
Queueing Networks ◽  
Smooth Surface ◽  
Network Models ◽  
Stress Release ◽  
Continuous Vector ◽  
Rice's Formula ◽  
Continuous Vector Field ◽  
Integral Curves ◽  
Piecewise Continuous ◽  
Rice’S Formula

Let X = {Xt: t ≥ 0} be a stationary piecewise continuous Rd-valued process that moves between jumps along the integral curves of a given continuous vector field, and let S ⊂ Rd be a smooth surface. The aim of this paper is to derive a multivariate version of Rice's formula, relating the intensity of the point process of (localized) continuous crossings of S by X to the distribution of X0. Our result is illustrated by examples relating to queueing networks and stress release network models.

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