Uniformly analytic solutions to a class of singular partial differential equations

Abstract

We study the singular nonlinear partial differential equation $ t\partial_tu = F(t, x, u, \partial_xu) $, where $ (t, x)\in\mathbb{R}\times\mathbb{R}^n $. Under some growth conditions on the coefficients of the partial Taylor expansion of $ F $, we construct the unique solution that is continuous in $ t $ and $ C^\infty $ in $ x $.

Keywords

• uniformly analytic functions
• singular partial differential equation