scholarly journals The hyperbolic Yang–Mills equation in the caloric gauge : local well-posedness and control of energy-dispersed solutions

2020 ◽  
Vol 2 (2) ◽  
pp. 233-384
Author(s):  
Sung-Jin Oh ◽  
Daniel Tataru
Keyword(s):  
Well Posedness ◽  
Yang Mills ◽  
And Control

Feedback theory to the well-posedness of evolution equations

2020 ◽  
Vol 378 (2185) ◽  
pp. 20190616
Author(s):  
S. Boulite ◽  
S. Hadd ◽  
L. Maniar
Keyword(s):  
Evolution Equations ◽  
Semigroup Theory ◽  
Well Posedness ◽  
Boundary Problems ◽  
Neutral Equations ◽  
Infinite Dimensional ◽  
Research Activities ◽  
Semigroup Approach ◽  
History Of ◽  
And Control

In this paper, we cross the boundary between semigroup theory and general infinite-dimensional systems to bridge the isolated research activities in the two areas. Indeed, we first give a chronological history of the development of the semigroup approach for control theory. Second, we use the feedback theory to prove the well-posedness of a class of dynamic boundary problems. Third, the obtained results are applied to the well-posedness of neutral equations with non-autonomous past. We will also see that the strong connection between semigroup and control theories lies in feedback theory, where different kinds of perturbations appear. This article is part of the theme issue ‘Semigroup applications everywhere’.

Corrigendum: Local well-posedness of the coupled Yang–Mills and Dirac system for low regularity data (2022 Nonlinearity 35 1)

Nonlinearity ◽  
2021 ◽  
Vol 35 (2) ◽  
pp. C3-C4
Author(s):  
Hartmut Pecher
Keyword(s):  
Well Posedness ◽  
Dirac System ◽  
Low Regularity ◽  
Yang Mills

Abstract An error in the proof of the main theorem is fixed.

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