Classical Solution of the First Mixed Problem for the Liouville Equation in a Half-Strip

Title	Classical Solution of the First Mixed Problem for the Liouville Equation in a Half-Strip
Authors	V. I. Korzyuk¹, J. V. Rudzko² ¹HSE University ²National Research Mordovia State University
Annotation	We consider a mixed problem for a nonlinear hyperbolic Liouville equation in a half-strip of the plane. We construct the solution in an implicit analytical form as a solution to some coupled integral equations. We prove the solvability of these integral equations using the Leray-Schauder theorem. We derive the corresponding a priori estimate by energy methods. For the problem under consideration, the uniqueness of the solution is proved, and conditions are established under which its classical solution exists.
Keywords	mixed problem, Liouville equation, hyperbolic equation, classical solution, matching conditions.
Citation	Korzyuk V. I., Rudzko J. V. ''Classical Solution of the First Mixed Problem for the Liouville Equation in a Half-Strip'' [Electronic resource]. Proceedings of the International Scientific Youth School-Seminar "Mathematical Modeling, Numerical Methods and Software complexes" named after E.V. Voskresensky (Saransk, July 29-31, 2025). Saransk: SVMO Publ, 2025. - pp. 292-293. Available at: https://conf.svmo.ru/files/2025/papers/paper60.pdf. - Date of access: 30.08.2025.