caa a22 4500 606194096 CHVBK 20210128100912.0 cr unu---uuuuu 210128e20150801xx s 000 0 eng 10.1007/s00030-014-0308-8 doi (NATIONALLICENCE)springer-10.1007/s00030-014-0308-8 The Benjamin-Bona-Mahony equation with dissipative memory [Elektronische Daten] [Filippo Dell'Oro, Youcef Mammeri, Vittorino Pata] We show that the nonlinear contraction semigroup generated by the Benjamin-Bona-Mahony equation with dissipative memory $$u_{t} - u_{txx} + u_{x} - \int_{0}^{\infty} g(s) u_{xx}(t-s)\, {\rm d}s + u^{p} u_{x} = 0$$ u t - u t x x + u x - ∫ 0 ∞ g ( s ) u x x ( t - s ) d s + u p u x = 0 is exponentially stable for every $${p\in\mathbb{N}}$$ p ∈ N . Springer Basel, 2014 Benjamin-Bona-Mahony equation nationallicence Nonlinear contraction semigroup nationallicence Dissipative memory nationallicence Exponential stability nationallicence Dell'Oro Filippo Institute of Mathematics of the Academy of Sciences of the Czech Republic, Žitná 25, 115 67, Prague 1, Czech Republic aut Mammeri Youcef Laboratoire Amiénois de Mathématique Fondamentale et Appliquée, CNRS UMR 7352, Université de Picardie Jules Verne, 80069, Amiens, France aut Pata Vittorino Dipartimento di Matematica "F. Brioschi”, Politecnico di Milano, Via Bonardi 9, 20133, Milan, Italy aut Nonlinear Differential Equations and Applications NoDEA Springer Basel 22/4(2015-08-01), 899-910 1021-9722 22:4<899 2015 22 30 https://doi.org/10.1007/s00030-014-0308-8 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00030-014-0308-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Dell'Oro Filippo Institute of Mathematics of the Academy of Sciences of the Czech Republic, Žitná 25, 115 67, Prague 1, Czech Republic aut NATIONALLICENCE 700 1- Mammeri Youcef Laboratoire Amiénois de Mathématique Fondamentale et Appliquée, CNRS UMR 7352, Université de Picardie Jules Verne, 80069, Amiens, France aut NATIONALLICENCE 700 1- Pata Vittorino Dipartimento di Matematica "F. Brioschi”, Politecnico di Milano, Via Bonardi 9, 20133, Milan, Italy aut NATIONALLICENCE 773 0- Nonlinear Differential Equations and Applications NoDEA Springer Basel 22/4(2015-08-01), 899-910 1021-9722 22:4<899 2015 22 30