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Uniqueness of weak solutions of 1+1 dimensional wave maps. (English) Zbl 0940.35141
The author studies the equations of wave maps from (1+1)-dimensional Minkowsky space to any complete Riemannian manifold. It is proved that a finite energy distributional solution to the Cauchy problem is unique. The technique is based on previous works on quasilinear hyperbolic systems. The result shows that the (1+1)-dimensional case is in sharp contrast with the (3+1)-dimensional one where the weak solutions are not unique.
MSC:
35L70Nonlinear second-order hyperbolic equations
58J45Hyperbolic partial differential equations on manifolds