Dynamics of a Cauchy problem related to extensible beams under nonlocal and localized damping effects

2021 ◽  
Vol 494 (1) ◽  
pp. 124620
Author(s):  
Sema Yayla ◽  
Camila L. Cardozo ◽  
Marcio A. Jorge Silva ◽  
Vando Narciso
Keyword(s):  
Cauchy Problem ◽  
Damping Effects ◽  
Localized Damping

Analysis of localized damping effects in channel flows with a periodic rough boundary

2017 ◽  
Vol 97 (6) ◽  
pp. 902-918 ◽  
Author(s):  
Jaewook Ahn ◽  
Jung-Il Choi ◽  
Kyungkeun Kang ◽  
Jihye Lim
Keyword(s):  
Channel Flows ◽  
Rough Boundary ◽  
Damping Effects ◽  
Localized Damping

Analysis of localized damping effects in channel flows with arbitrary rough boundary

2018 ◽  
Vol 98 (13) ◽  
pp. 2359-2377 ◽  
Author(s):  
Jaewook Ahn ◽  
Jung-Il Choi ◽  
Kyungkeun Kang ◽  
Jae-Myoung Kim
Keyword(s):  
Channel Flows ◽  
Rough Boundary ◽  
Damping Effects ◽  
Localized Damping

How a sheperd guides a sheep herd?

1984 ◽  
Vol 75 ◽  
pp. 331-337
Author(s):  
Richard Greenberg
Keyword(s):  
Point Of View ◽  
Single Ring ◽  
Damping Effects ◽  
Ring Particle

ABSTRACTThe mechanism by which a shepherd satellite exerts a confining torque on a ring is considered from the point of view of a single ring particle. It is still not clear how one might most meaningfully include damping effects and other collisional processes into this type of approach to the problem.

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.

The Resolvent Operator

2017 ◽  
Author(s):  
Charles L. Epstein ◽  
Rafe Mazzeo
Keyword(s):  
Cauchy Problem ◽  
Heat Equation ◽  
Laplace Transform ◽  
Heat Kernel ◽  
Resolvent Operator ◽  
Contour Integration ◽  
Resolvent Kernel ◽  
The Laplace Transform ◽  
Elliptic Estimates ◽  
The Resolvent Operator

This chapter describes the construction of a resolvent operator using the Laplace transform of a parametrix for the heat kernel and a perturbative argument. In the equation (μ‎-L) R(μ‎) f = f, R(μ‎) is a right inverse for (μ‎-L). In Hölder spaces, these are the natural elliptic estimates for generalized Kimura diffusions. The chapter first constructs the resolvent kernel using an induction over the maximal codimension of bP, and proves various estimates on it, along with corresponding estimates for the solution operator for the homogeneous Cauchy problem. It then considers holomorphic semi-groups and uses contour integration to construct the solution to the heat equation, concluding with a discussion of Kimura diffusions where all coefficients have the same leading homogeneity.

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