  We study a family of nonlinear initial value partial differential equations
in the complex domain under the action of two asymmetric time variables.
Different Gevrey bounds and multisummability results are obtain depending on
each element of the family, providing a more complete picture on the asymptotic
behavior of the solutions of PDEs in the complex domain in several complex
variables.
  The main results lean on a fixed point argument in certain Banach space in
the Borel plane, together with a Borel summability procedure and the action of
different Ramis-Sibuya type theorems.
