In this paper, we consider some classes of non linear partial differential equations with regular singularity and irregular singularity with respect to t=0 and x=0 respectively. Our purpose is to establish a result similar to the k-summability known in the case of singular ordinary differential equations. It's shown that, under some generic type conditions (holomorphic to t), all formal solutions are Borel summable or k-summable with respect to xin all directions except at most a countable number.