Approximate solutions of vector fields and an application to Denjoy-Carleman regularity of solutions of a nonlinear PDE

Nicholas Braun Rodrigues, Antonio V. da Silva

In this paper we study microlocal regularity of a ${\mathcal{C}}^2$ solution $u$ of the equation \begin{equation*} u_t = f(x,t,u,u_x), \end{equation*} where $f(x,t,{\zeta }_0,\zeta )$ is ultrad…