Global classical solvability of a problem with nonlocal conditions for degenerate hyperbolic system of the first order equations

Author R. V. Andrusyak, V. M. Kyrylych, O. V. Peliushkevych
ru.andrusyak@gmail.com, vkyrylych@ukr.net, olpelushkevych@ukr.net
Ivan Franko National University of Lviv

Abstract Using the method of characteristics and the Banach fixed point theorem we established the existence and uniqueness of a global classical (smooth) solution to an initial-boundary value problem with nonlocal boundary conditions for a hyperbolic integro-differential system involving equations without time derivative of unknown functions.
Keywords hyperbolic system; method of characteristics; Banach theorem; fixed point
Reference 1. B.L. Rozhdestvenskii, N.N. Yanenko, Systems of quasilinear equations and their applications to gas dynamics, Moscow, Nauka, 1978. (in Russian)

2. A.G. Kulikovskii, N.V. Pogorelov, A. Yu. Semenov, Mathematical aspects of the numerical solution to hyperbolic systems of equations, Moscow, Fizmatlit, 2001. (in Russian)

3. A.V. Arguchintsev, Optimal control of hyperbolic systems, Moscow, Fizmatlit, 2007. (in Russian)

4. D.S. Lapin, A.M. Filimonov, Mixed problem for singular quasilinear hyperbolic systems with a single spatial variable, Mat. Zametki, 73 (2003), ¹2, 315-318. (in Russian)

5. V.M. Kyrylych, A.M. Filimonov, Generalized continuous solvability of the problem with unknown boundaries for singular hyperbolic systems of quasilinear equations, Mat. Stud., 30 (2008), ¹1, 42–60. (in Russian)

6. R.V. Andrusyak, V.M. Kyrylych, O.V. Peliushkevych, The problem for singular hyperbolic system in angular domain, Applied problems of mechanics and mathematics, 9 (2011), 15–22. (in Ukrainian)

7. O. Maulenov, A.D. Myshkys, About solvability of mixed problem for degenerated semilinear hyperbolic system on the interval, Izv. AN Kaz. SSR, Ser. Fiz.-mat., 5 (1981), 25–29. (in Russian)

Pages 80-92
Volume 38
Issue 1
Year 2012
Journal Matematychni Studii
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