What question did this study set out to answer?

The aim is to investigate a problem with modified boundary conditions for the Gellerstedt equation to ensure correctness.

March 1, 2026

Combined Problem with Local and Nonlocal Conditions and with General Conjugation Conditions for the Gellerstedt Equation with a Singular Coefficient

Key Points

The aim is to investigate a problem with modified boundary conditions for the Gellerstedt equation to ensure correctness.
Examined the Tricomi problem with specified boundary conditions.
Introduced a nonlocal condition replacing the missing Tricomi condition.
Specified a general conjugation condition on the degeneracy segment.
Established the correctness of the modified problem under the new conditions.
Demonstrated that the nonlocal conditions effectively address the missing boundary constraints.

Abstract

In the Tricomi problem, the value of the desired function is specified at all points of the boundary characteristic. In this paper, we study the correctness of the problem where part of the boundary characteristic is freed from the boundary condition and this missing Tricomi condition is replaced by a nonlocal condition with displacement on the internal characteristic and on the part of the boundary characteristic. On the degeneracy segment, a general conjugation condition is specified.

KI fragen

Bookmark