Аннотация:
We consider the Riemann–Hilbert problem
in a domain of complicated shape (the exterior of a system of cuts),
with the condition of growth of the solution at infinity.
Such a problem arises in the Somov model of the effect
of magnetic reconnection in the physics of plasma,
and its solution has the physical meaning of a magnetic field.
The asymptotics of the solution is obtained for the case of infinite extension
of four cuts from the given system,
which have the meaning of shock waves, so that
the original domain splits into four disconnected components in the limit.
It is shown that if the coefficient in the condition of growth of the magnetic field at
infinity
consistently decreases in this case,
then this field basically coincides in the limit
with the field arising in the Petschek model of the effect
of magnetic reconnection.
Ключевые слова:Riemann–Hilbert problem, conformal mapping,
singular deformation of a domain, asymptotics of a solution,
effect of magnetic reconnection, Somov model, Petschek model.
Список цитирования
