  This work is concerned with establishing the existence and uniqueness of the
solution to a mixed-type degenerate boundary value problem for a relativistic
magnetohydrodynamics system. We first consider a full relativistic
magnetohydrodynamics system and reduce it to a simplified form under the
assumption that the magnetic field vector is orthogonal to the velocity vector.
We consider a boundary value problem for the steady part of this reduced system
where the boundary data is prescribed on a sonic boundary and a characteristic
curve. Here the main difficulty is the consideration of a relativistic system,
with a general equation of state while considering the magnetic field effects
as well, which we believe has never been analyzed before in the context of the
analytical study of sonic-supersonic flows. Also, the degeneracy of the
governing equations along the sonic curve is a crucial challenge. However, we
employ the iteration method used in the work of Li and Hu
\cite{li2019degenerate} to prove the existence and uniqueness of a local
classical supersonic solution in the partial hodograph plane first and finally,
we recover a local smooth solution to the boundary value problem in the
physical plane by applying an inverse transformation.
