An analogue of the Tricomi problem for a mixed type of quasilinear equation with two lines of degeneracy

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Abstract

The paper proves the unique solvability of an analog of the Tricomi problem for a quasilinear equation of mixed type with two lines of degeneracy. The class R1 of generalized solutions in the hyperbolic part of the domain is introduced. The uniqueness of the solution is proved by the method of energy integrals. The existence of a solution is proved by the method of integral equations. The boundary value problem is reduced to an equivalent system of integral equations, the solvability of which is proved using the Schauder principle. As a result, the application of the Schauder principle resulted in the global solvability of the problem under study without any restrictions on the size of the area of the region under consideration and on the value of the given functions.

About the authors

Xaydar R. Rasulov

Bukhara Branch of the Institute of Mathematics named after V. I. Romanovskiy at the Academy of Sciences of the Republic of Uzbekistan; Bukhara State University

Author for correspondence.
Email: xrasulov71@mail.ru
ORCID iD: 0000-0001-8525-4701
Scopus Author ID: 57359417100
http://www.mathnet.ru/person191178

Cand. Phys. & Math. Sci., Associate Professor; Leading Researcher

Uzbekistan, 705018, Bukhara, Muhammad Igbol st., 11

References

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