Approximation of Ill-posed Boussinesq Equations
نویسندگان
چکیده
In this paper we study finite dimensional approximations to Boussinesq type equations. Our methods are based on infinite dimensional center manifold theory. The main advantage of our approach is that we can handle both well-posed and ill-posed versions of the Boussinesq equation. We show that for suitable initial conditions, our approximations describe the dynamics accurately for long enough times. Furthermore, the PDEs are reduced to linear ODEs.
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