A gap metric perspective of well-posedness for nonlinear feedback interconnections

2013 ◽  
Author(s):  
Sei Zhen Khong ◽  
Michael Cantoni ◽  
Jonathan H. Manton
Keyword(s):  
Well Posedness ◽  
Nonlinear Feedback ◽  
Gap Metric ◽  
Feedback Interconnections

scholarly journals Well-posedness of infinite-dimensional linear systems with nonlinear feedback

2019 ◽  
Vol 128 ◽  
pp. 19-25 ◽  
Author(s):  
Anthony Hastir ◽  
Federico Califano ◽  
Hans Zwart
Keyword(s):  
Linear Systems ◽  
Well Posedness ◽  
Nonlinear Feedback ◽  
Infinite Dimensional

Well-posedness and a general decay for a nonlinear damped porous thermoelastic system with second sound

2019 ◽  
Vol 26 (1) ◽  
pp. 1-11 ◽  
Author(s):  
Mohammad M. Al-Gharabli ◽  
Salim A. Messaoudi
Keyword(s):  
Decay Rate ◽  
Convex Functions ◽  
Semigroup Theory ◽  
General Decay ◽  
Well Posedness ◽  
Second Sound ◽  
Nonlinear Feedback ◽  
Damping Term ◽  
General Decay Rate ◽  
One Dimensional

Abstract In this paper, we consider a one-dimensional porous thermoelastic system with second sound and nonlinear feedback. We show the well-posedness, using the semigroup theory, and establish an explicit and general decay rate result, using some properties of convex functions and the multiplier method. Our result is obtained without imposing any restrictive growth assumption on the damping term.

Cauchy Problem for Equations with Fractional Differentiation Bessel Operator in the Space of Temperate Distributions

2003 ◽  
Vol 8 (1) ◽  
pp. 61-75
Author(s):  
V. Litovchenko
Keyword(s):  
Functional Analysis ◽  
Cauchy Problem ◽  
Fundamental Solution ◽  
Initial Function ◽  
Well Posedness ◽  
Fractional Differentiation ◽  
Basic Tool ◽  
Conjugate Space ◽  
Analysis Technique ◽  
The Cauchy Problem

The well-posedness of the Cauchy problem, mentioned in title, is studied. The main result means that the solution of this problem is usual C∞ - function on the space argument, if the initial function is a real functional on the conjugate space to the space, containing the fundamental solution of the corresponding problem. The basic tool for the proof is the functional analysis technique.

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