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On the global existence and small dissipation limit for generalized dissipative Zakharov system
Author(s) -
Wang Xueqin,
Shang Yadong
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4859
Subject(s) - dissipative system , mathematics , uniqueness , dissipation , convergence (economics) , limit (mathematics) , mathematical analysis , galerkin method , weak solution , boundary value problem , a priori and a posteriori , initial value problem , a priori estimate , nonlinear system , physics , thermodynamics , philosophy , epistemology , quantum mechanics , economics , economic growth
This paper deals with the existence and uniqueness of the global solutions to the initial boundary value problem for a generalized Zakharov system with direct self‐interaction of the dispersive waves and weak dissipation in the nondispersive subsystem. We prove the global existence of the generalized solution to the problem by a priori estimates and Galerkin method. We also establish the regularity of the global generalized solution and the existence and uniqueness of the global classical solution. Moreover, we obtain the convergence of the solutions of the generalized Zakharov system with dissipation as the dissipative coefficient approaches zero.