Well-posedness for a linear Benjamin-Bona-Mahony-Burgers equation with periodic boundary conditions
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Abstract
This article is concerned with the study of the solutions of a linear Benjamin-Bona-Mahony-Burgers (BBMB) equation. We show that the initial value problem is well-posed in periodic Sobolev spaces Hsp (0,2 π), for all s ∈ R, in the sense that we establish global existence and uniqueness theorems for this equation.
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References
Arora, S., Jain, R., & Kukreja, V.K. (2020). Solution of Benjamin-Bona-Mahony-Burgersequation using collocation methodwith quintic Hermite splines. Applied Numerical Mathematics, 154, 1-16. https://doi.org/10.1016/j.apnum.2020.03.015.
Benjamin, T. B., Bona, J. L., & Mahony, J. J. (1972). Model equations for long waves in nonlinear dispersive systems, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences,272(1220), 47-78. https://doi.org/10.1098/rsta.1972.0032.
Burgers, J. M. (1948). A mathematical model illustrating the theory ofturbulence. Advances in Applied Mechanics, 1, 171-199. https://doi.org/10.1016/S0065-2156(08)70100-5[4].
Cazenave, T., & Haraux, A. (1999). An introduction to semilinear evolution equations, Oxford Lecture Series in Mathematics and its Applications, 13, The Clarendon Press, Oxford University Press, New York.
Korteweg, D. J. & de Vries, G. (1985). On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 39(240), 422-443. https://doi.org/10.1080/14786449508620739.
Micu, S. & Pazoto, A. F. (2017). Stabilization of a Boussinesq system with generalized damping, Systems Control Lett. 105, 62-69. https://doi.org/10.1016/j.sysconle.2017.04.012.
Pazy, A. (1983). Semigroups of Linear Operators and Applications to Partial Differential Equations, Applied Mathematical Sciences, Vol. 44, Springer-Verlag: New York-Berlin-Heidelberg-Tokyo.http://dx.doi.org/10.1007/978-1-4612-5561-1.
Zhang, Q., & Liu, L. (2021). Convergence and Stability in Maximum Norms of Linearized Fourth-Order Conservative Compact Scheme for Benjamin–Bona–Mahony–Burgers’ Equation, Journal of Scientific Computing, 87(59). https://doi.org/10.1007/s10915-021-01474-3.