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.

Dans ce papier, nous calculons l'indice de Gevrey formelle de solution formelle d'une classe d'

In this paper, we study a class of nonlinear higher order partial differential equations with irregular singularities in complex domain Ct

In this paper, we study the local existence and uniqueness of classical solutions to a wide class of systems of chemotaxis equations. These systems are essentially quasilinear strongly coupled partial differential equations. We also study the maximal interval of existence in time of solutions. The results are illustrated in application to a number of partial differential equation models arising in biology.

In this paper, we study a class of non-linear singular partial differential equation in complex domain Ct