ar X iv : 0 90 4 . 24 27 v 1 [ m at h . O C ] 1 6 A pr 2 00 9 Remarks on the Controllability of Some Quasilinear Equations ∗
نویسنده
چکیده
In this Note, we review the main existing results, methods, and some key open problems on the controllability of nonlinear hyperbolic and parabolic equations. Especially, we describe our recent universal approach to solve the local controllability problem of quasilinear time-reversible evolution equations, which is based on a new unbounded perturbation technique. It is also worthy to mention that the technique we develop can also be applied to other problems for quasilinear equations, say local existence, stabilization, etc.
منابع مشابه
ar X iv : 0 90 7 . 41 78 v 1 [ m at h . PR ] 2 3 Ju l 2 00 9 An Introduction to Stochastic PDEs
2 Some Motivating Examples 2 2.1 A model for a random string (polymer) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 The stochastic Navier-Stokes equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.3 The stochastic heat equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.4 What have we learned? . . . . . . . . . . . . . . . . . . . . . ...
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