Energy-based analysis of evolution equations

• Applicant: Professorin Dr. Birgit Jacob
• Subject Area: Mathematics
• Term: from 2012 to 2017
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 214819299

• Final Report Year: 2017

Final Report Abstract

Hamiltonian dynamics is a well-known topic within mathematics and physics. Combining this concept with concepts from system and control theory has led to the port-Hamiltonian system class. For systems described by ordinary differential equations this approach is well-studied and has resulted in new control strategies. For systems described by partial differential equations there are several promising approaches, but the theory is much less mature than for ordinary differential equations. In this project we used energy-bases analysis to receive new results for evolution equations with energy conservation and with evolution equations with energy dissipation. In particular, the questions of well-posedness and stability are addressed.

Publications

• Stability and Stabilization of Infinitedimensional Linear Port-Hamiltonian Systems. Evolution Equations and Control Theory (EECT) 3(2) (2014), 207-229
  Björn Augner and Birgit Jacob
  (See online at https://doi.org/10.3934/eect.2014.3.207)
• Evolution equations governed by Lipschitz continuous non-autonomous forms. Czechoslovak Math. J. 65(140) (2015), no. 2, 475-491
  Ahmed Sani and Hafida Laasri
  (See online at https://doi.org/10.1007/s10587-015-0188-z)
• On the right multiplicative perturbation of non-autonomous Lp-maximal regularity. Journal of Operator Theory 74 (2) (2015), 391-415
  Björn Augner, Birgit Jacob and Hafida Laasri
  (See online at https://dx.doi.orgOn the right multiplicative perturbation of non-autonomous Lp-maximal regularity. Journal of Operator Theory 74 (2) (2015), 391-415/10.7900/jot.2014jul31.2064 )
• Well-posedness and Stability of Linear Port-Hamiltonian Systems with Nonlinear Boundary Feedback
  Björn Augner
  
• Stabilisation of Infinite-Dimensional Port-Hamiltonian Systems via Dissipative Boundary Feedback, PhD thesis, Juni 2016
  Björn Augner
  
• Well-posedness of networks od 1-D hyperbolic partial differential equations
  Birgit Jacob and Julia T. Kleinhans