In the theory of ordinary differential equation the existence of center-stable manifolds is well-understood. In the theory of partial differential equations this topic is relatively new. Recently the authors (partly in cooperation with others) have shown that for certain energy subcritical equations the center-stable manifold associated with the ground state appears as a hypersurface which separates a region of finite-time blowup from one which exhibits global solutions which scatter to zero. The book gives a complete, self-contained proof of this novel result for radial solutions of the cubic, focusing, Klein-Gordon equation in three spatial dimensions. Some extensions to nonradial solutions and other equations are sketched in the final chapter.
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