Non-smooth solutions of Euler ? Lagrange equations corresponding to variational problems with several unknown functions of several variables and quadratic functional are studied. Propagation of weak discontinuities is described by equations of the method of singular characteristics, developed by A.A. Melikyan. The occurrence and interaction of weak discontinuities of solutions initiated by non-smooth initial conditions are studied. The proposed methodology allows us to study the propagation and interaction of weak waves
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