  In the core accretion model, planetesimals grow by mutual collisions and
engulfing millimeter-to-centimeter particles, i.e., pebbles. Pebble accretion
can significantly increase the accretion efficiency and help explain the
presence of planets on wide orbits. However, the pebble supply is typically
parameterized as a coherent pebble mass flux, sometimes being constant in space
and time. Here we solve the dust advection and diffusion within viciously
evolving protoplanetary disks to determine the pebble supply self-consistently.
The pebbles are then accreted by planetesimals interacting with the gas disk
via gas drag and gravitational torque. The pebble supply is variable with space
and decays with time quickly, with a pebble flux below 10 $M_\oplus$ Myr$^{-1}$
after 1 Myr in our models. As a result, only when massive planetesimals ($>$
0.01 $M_\oplus$) are luckily produced by the streaming instability or the disk
has low viscosity ($\alpha \sim 0.0001$) can the herd of planetesimals grow
over a Mars mass within 2 Myr. By then, planetesimals only capture pebbles
about 50 times their mass and as little as 10 times beyond 20 au due to limited
pebble supply. Further studies considering multiple dust species in various
disk conditions are warranted to fully assess the realistic pebble supply and
its influence on planetesimal growth.
