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Well posedness for the nonlinear Klein-Gordon-Schrödinger equations with heterointeractions. (English) Zbl 1309.35143

Summary: In this paper we study the well posedness of solution to a certain system of nonlinear Klein-Gordon-Schrödinger equations in three space dimensions. Basing on the Strichartz estimates, we obtain the global existence, uniqueness of the solutions, and continuous dependence with respect to initial data in the Sobolev spaces of low regularities by setting appropriate contraction and taking difference estimates.{
©2010 American Institute of Physics}

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness
46E39 Sobolev (and similar kinds of) spaces of functions of discrete variables
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