Global solvability of one-dimensional Cauchy problem for the system of magnetic gas dynamics with arbitrary initial conditions

Cauchy problem for the equations system describing one-dimensional ionized gas flow under conditions of the magnetic gas dynamics approximation is considered. The initial data is admitted to be functions with an arbitrary amplitude whose left and right limits are different. An approximate method of solving the problem is constructed, its convergence is established and thus global solvability in the class of functional solutions of the problem considered is proved.