TL;DR
This paper discusses the Tricomi equation, a second-order PDE of mixed type, highlighting its mathematical properties, transformations, and connections to physical phenomena like transonic flow.
Contribution
It provides an overview of the Tricomi equation's properties, transformations, and its relation to other equations such as the Euler-Poisson-Darboux and Keldysh equations.
Findings
Analyzes the well-posedness of boundary value problems for the Tricomi equation.
Explores transformations into elliptic and hyperbolic forms.
Highlights connections to transonic flow and isometric embedding.
Abstract
The Tricomi equation is a second-order partial differential equation of mixed elliptic-hyperbolic type. It was first analyzed in the work by Francesco Giacomo Tricomi (1923) on the well-posedness of a boundary value problem. The Tricomi equation can be transformed into the corresponding elliptic or hyperbolic Euler-Poisson-Darboux equation, and has a close connection with transonic flow and isometric embedding. It has different degeneracy from a closely related equation, the Keldysh equation.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsNonlinear Waves and Solitons · Numerical methods for differential equations