On Solvability of a Poincare–Tricomi Type Problem for an Elliptic–Hyperbolic Equation of the Second Kind
2021
In this paper we study a boundary value problem with the
Poincare–Tricomi condition for a degenerate partial differential
equation of elliptic-hyperbolic type of the second kind. In the
hyperbolic part of a degenerate mixed differential equation of the
second kind the line of degeneracy is a characteristic. For this
type of differential equations a class of generalized solutions is
introduced in the characteristic triangle. Using the properties of
generalized solutions, the modified Cauchy and Dirichlet problems
are studied. The solutions of these problems are found in the
convenient form for further investigations. A new method has been
developed for a differential equation of mixed type of the second
kind, based on energy integrals. Using this method, the uniqueness
of the considering problem is proved. The existence of a solution
of the considering problem reduces to investigation of a singular
integral equation and the unique solvability of this problem is
proved by the Carleman–Vekua regularization method.
Keywords:
- Correction
- Source
- Cite
- Save
- Machine Reading By IdeaReader
18
References
5
Citations
NaN
KQI