  The ring-like structures in protoplanetary discs that are observed in the
cold dust emission by ALMA, might be explained by dust aggregates trapped
aerodynamically in pressure maxima. The effect of a transient pressure maximum
is investigated that develops between two regimes with different turbulent
levels. We study how such a pressure maximum collects dust aggregates and
transforms them into large planetesimals and Moon-mass cores that can further
grow to a few Earth-mass planets by pebble accretion, and eventually to giant
planets, by considering the accretion of a gaseous envelope. A numerical model
is developed, incorporating the evolution of gaseous disc, growth and transport
of pebbles, N-body interactions of growing planetary cores and their
backreaction to gas disc by opening a partial gap. Planetesimal formation by
streaming instability is parametrized in our model. A transient pressure
maximum efficiently accumulates dust particles that can grow larger than
mm-size. If this happens, dust aggregates can be transformed by the streaming
instability process into such large planetesimals, which can grow further by
pebble accretion, according to our assumptions. As the gas evolves to its
steady state, the pressure maximum vanishes, and the concentrated pebbles that
are not transformed to planetesimals and accreted by the growing planet, drift
inward. During this inward drift, if the conditions of the streaming
instability are met, planetesimals are formed in a wide radial range of the
disc. Conclusions. A transient pressure maximum is a favourable place for
planetesimal and planet formation during its lifetime and the concentration of
pebbles induces continuous formation of planetesimals even after its
disappearance. Besides, the formation of a planet can trigger the formation of
planetesimals over a wide area of the protoplanetary disc.
