caa a22 4500 605525161 CHVBK 20210128100757.0 cr unu---uuuuu 210128e20150801xx s 000 0 eng 10.1007/s10958-015-2471-9 doi (NATIONALLICENCE)springer-10.1007/s10958-015-2471-9 Baghaturia G. N. Muskhelishvili Institute of Computational Mathematics, Georgian Technical University, Tbilisi, Georgia aut Nonlinear Versions of Hyperbolic Problems for One Quasi-Linear Equation of Mixed Type [Elektronische Daten] [G. Baghaturia] The Cauchy and Goursat problems for a quasi-linear second-order hyperbolic equation with admissible order and type degeneracy are considered. The conditions for nonexistence of a solution of the Cauchy problem are established. However, in conditions of the existence, the solution of the problem is constructed explicitly. In addition, nonlinear versions of the Goursat problem are examined and solutions of these problems are constructed in the explicit form. For the Cauchy problem, as well as for both of the characteristic problems, the structure of the domain of definition of the solution is described. Springer Science+Business Media New York, 2015 Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 208/6(2015-08-01), 621-634 1072-3374 208:6<621 2015 208 10958 https://doi.org/10.1007/s10958-015-2471-9 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10958-015-2471-9 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Baghaturia G. N. Muskhelishvili Institute of Computational Mathematics, Georgian Technical University, Tbilisi, Georgia aut NATIONALLICENCE 773 0- Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 208/6(2015-08-01), 621-634 1072-3374 208:6<621 2015 208 10958