The Cauchy problem for fully nonlinear parabolic systems on manifolds
Abstract
We show the short-time existence and uniqueness of solutions to the Cauchy problem for fully nonlinear systems of arbitrary even order on closed manifolds which are strongly parabolic at the initial values. The proof uses a linearization procedure and a fixed-point argument, and the key ingredient is the well known Schauder estimates for linear, strongly parabolic systems.
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Advanced Mathematical Modeling in Engineering
Advanced Mathematical Physics Problems
Publication details
- Journal / source
- SSRN Electronic Journal
- Publisher
- Elsevier BV
- Publication date
- 1 January 2026
- Language
- EN
- Document type
- Preprint