Abstract
We consider the viscous Camassa–Holm equation in a one-dimensional torus. We prove that we can steer the solution of the equation to a constant steady state at any given time, using a localized interior control, when initial condition is in a small ball near the constant steady state.
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Acknowledgements
The author would like to thank Prof. Mythily Ramaswamy for useful discussions. The author is grateful to the referee for valuable comments which improved the manuscript. The author acknowledges the financial support from the Airbus Group Corporate Foundation Chair in Mathematics of Complex Systems established in TIFR, Bangalore.
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Mitra, D. Local null controllability of viscous Camassa–Holm equation. J. Evol. Equ. 18, 627–657 (2018). https://doi.org/10.1007/s00028-017-0414-2
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DOI: https://doi.org/10.1007/s00028-017-0414-2