A note on the nonlinear derived Cauchy problem

2022/11/09 by Paugam, Frédéric
#Algebraic Geometry (math.AG) #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2211.04860

Abstract

We define and study a generalization of the analytic Cauchy problem, that specializes to the Cauchy-Kowaleskaya-Kashiwara problem in the linear case. The main leitmotive of this text is to adapt Kashiwara's formulation of this problem both to the relatively D-algebraic case and to the derived analytic situation. Along the way, we define the characteristic variety of a derived nonlinear partial differential system.

Related

• Derived Moduli Spaces of Nonlinear PDEs I: Singular Propagations
• A generalisation of the Cauchy-Kovalevskaia theorem
• A Cauchy-Kowalevsky theorem for overdetermined systems of nonlinear partial differential equations and geometric applications
• Exact linear representations of the nonlinear Cauchy problems and their smooth solutions
• On the geometry of the domain of the solution of nonlinear Cauchy problem