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The unit condition and global existence for a class of nonlinear Klein- Gordon equations. (English) Zbl 0781.35062
Summary: Global existence for a special class of nonlinear Klein-Gordon equations in two space dimensions is proved. In particular it is shown that, for small initial data, the equation \(\partial_{tt} u-\Delta u+ u= u^ 2\) has a global solution.

MSC:
35Q53 KdV equations (Korteweg-de Vries equations)
35L15 Initial value problems for second-order hyperbolic equations
35B65 Smoothness and regularity of solutions to PDEs
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