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Exponential boundary feedback stabilization of a shock steady state for the inviscid Burgers equation
- Source :
- Mathematical Models and Methods in Applied Sciences, Vol. 29, no.02, p. 271-316 (2019), Mathematical Models and Methods in Applied Sciences, Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 2019, 29 (2), pp.271-316. ⟨10.1142/S021820251950009X⟩, Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 2019, 29 (2), pp.271-316, Mathematical Models and Methods in Applied Sciences, 2019, 29 (2), pp.271-316. ⟨10.1142/S021820251950009X⟩
- Publication Year :
- 2019
- Publisher :
- World Scientific Pub Co Pte Lt, 2019.
-
Abstract
- In this paper, we study the exponential stabilization of a shock steady state for the inviscid Burgers equation on a bounded interval. Our analysis relies on the construction of an explicit strict control Lyapunov function. We prove that by appropriately choosing the feedback boundary conditions, we can stabilize the state as well as the shock location to the desired steady state in [Formula: see text]-norm, with an arbitrary decay rate.
- Subjects :
- 0209 industrial biotechnology
Steady state (electronics)
boundary feedback controls
Applied Mathematics
010102 general mathematics
Mathematical analysis
Boundary (topology)
02 engineering and technology
01 natural sciences
Burgers equation
Shock (mechanics)
Exponential function
Burgers' equation
020901 industrial engineering & automation
Inviscid flow
Modelling and Simulation
Modeling and Simulation
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
Boundary value problem
0101 mathematics
shock steady state
Control-Lyapunov function
Mathematics
Subjects
Details
- ISSN :
- 17936314 and 02182025
- Volume :
- 29
- Database :
- OpenAIRE
- Journal :
- Mathematical Models and Methods in Applied Sciences
- Accession number :
- edsair.doi.dedup.....1fc9d445b98076ccc4c450b32ba63964