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The global well-posedness of the initial-value problem associated to the coupled system of BBM-Burgers equations (*) in the classical Sobolev spaces Hs(R) x Hs(R) for s ≥ 2 is studied. Furthermore we find decay estimates of the solutions of (*) in the norm Lq(R) x Lq(R), 2 ≤ q ≤ ∞ for general initial data. Model (*) is motivated by a work due to Gear and Grimshaw [10] who considered strong interaction of weakly nonlinear long waves governed by a coupled system of KdV equations.
Morais Pereira, Jardel. "Global existence and decay of solutions of a coupled system of BBM-Burgers equations.." Revista Matemática Complutense 13.2 (2000): 423-443. <http://eudml.org/doc/44359>.
@article{MoraisPereira2000, abstract = {The global well-posedness of the initial-value problem associated to the coupled system of BBM-Burgers equations (*) in the classical Sobolev spaces Hs(R) x Hs(R) for s ≥ 2 is studied. Furthermore we find decay estimates of the solutions of (*) in the norm Lq(R) x Lq(R), 2 ≤ q ≤ ∞ for general initial data. Model (*) is motivated by a work due to Gear and Grimshaw [10] who considered strong interaction of weakly nonlinear long waves governed by a coupled system of KdV equations.}, author = {Morais Pereira, Jardel}, journal = {Revista Matemática Complutense}, keywords = {Problema de Cauchy; Problemas hiperbólicos; Sistemas no lineales; global well-posedness; Sobolev spaces; decay estimates; interaction of weakly nonlinear long waves}, language = {eng}, number = {2}, pages = {423-443}, title = {Global existence and decay of solutions of a coupled system of BBM-Burgers equations.}, url = {http://eudml.org/doc/44359}, volume = {13}, year = {2000}, }
TY - JOUR AU - Morais Pereira, Jardel TI - Global existence and decay of solutions of a coupled system of BBM-Burgers equations. JO - Revista Matemática Complutense PY - 2000 VL - 13 IS - 2 SP - 423 EP - 443 AB - The global well-posedness of the initial-value problem associated to the coupled system of BBM-Burgers equations (*) in the classical Sobolev spaces Hs(R) x Hs(R) for s ≥ 2 is studied. Furthermore we find decay estimates of the solutions of (*) in the norm Lq(R) x Lq(R), 2 ≤ q ≤ ∞ for general initial data. Model (*) is motivated by a work due to Gear and Grimshaw [10] who considered strong interaction of weakly nonlinear long waves governed by a coupled system of KdV equations. LA - eng KW - Problema de Cauchy; Problemas hiperbólicos; Sistemas no lineales; global well-posedness; Sobolev spaces; decay estimates; interaction of weakly nonlinear long waves UR - http://eudml.org/doc/44359 ER -