Methods of construction and study of Frankl system self-similar solutions in the hyperbolic case

11th International Conference on "Mesh methods for boundary-value problems and applications"

Shemyakina, T.^1 ; Alekseenko, S.^2

Peter the Great Saint-Petersburg Polytechnical University, 29 Politechnicheskaya Street, Saint-Petersburg

195251, Russia^1

Nizhny Novgorod State Technical University N A R e Alekseev, 24 Minin Street, Nizhny Novgorod

603950, Russia^2

关键词: Global classical solution;    Irrotational motion;    Methods of constructions;    Mixed type equations;    Numerical experiments;    Numerical solution;    Self-similar solution;    Supersonic speed;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/158/1/012085/pdf
DOI  :  10.1088/1757-899X/158/1/012085

来源: IOP

【 摘 要 】

Self-similar solution of the Frankl system in the hyperbolic case was found. The Frankl system is a system of mixed type equations. Under certain conditions, it describes a model of the membrane theory of shells. The Frankl system describes a stationary irrotational motion of an ideal gas in the transition vicinity from subsonic to supersonic speeds. We find a sufficient condition on the initial data that guarantees existence of a global classical solution continued from a local solution. The proof of the nonlocal solvability of the problem in the original variables is based on the additional argument method. It allowed justify and construct a numerical solution. Numerical experiments were carried out for model examples of the Frankl system.