References

  1. Al-Droubi A., Renardy M. Energy methods for a parabolic-hyperbolic interface problem arising in electromagnetism. Z. Angew. Math. Phys. 1988, 39 (6), 931–936. doi:10.1007/BF00945129
  2. Ashyralyev A., Ozdemir Y. On nonlocal boundary value problems for hyperbolic-parabolic equations. Taiwanese J. Math. 2007, 11 (4), 1075–1089. doi:10.1007/978-1-4020-5678-9_9
  3. Ashyralyev A., Yurtsever A. On a nonlocal boundary value problem for semilinear hyperbolic-parabolic equations. Nonlinear Anal., Theory Methods Appl. 2001, 47 (5), 3585–3592. doi:10.1016/S0362-546X(01)00479-5.
  4. Bhargava A., Chanmugam A., Herman C. Heat transfer model for deep tissue injury: a step towards an early thermographic diagnostic capability. Diagn. Path. 2014, 9, article 36. doi:10.1186/1746-1596-9-36
  5. Bobyk I., Symotyuk M. Problem with two multiple points of interpolation for linear factorized partial differential equations. Visn. Nats. Univ. L’viv. Politekh., Fiz.-Mat. Nauky 2010, 687, 11–19. (in Ukrainian).
  6. Bouziani A. Solution of a transmission problem for semilinear parabolic-hyperbolic equations by the time-discretization method. Int. J. Stoch. Anal. 2006, 2006, 1–23. doi:10.1155/JAMSA/2006/61439
  7. Chandra T.K. The Borel-Cantelli lemma. Springer, New Delhi, 2016.
  8. Chen S. Mixed type equations in gas dynamics. Q. Appl. Math. 2010, 68 (3), 487–511. doi:10.1090/S0033-569X-2010-01164-9
  9. Liu Ch., Ball W.P. Analytical modeling of diffusion-limited contamination and decontamination in a two-layer porous medium. Adv. Water Resour. 1998, 21 (4), 297–313. doi:10.1016/S0309-1708(96)00062-0
  10. Harman G. Metric number theory. Oxford University Press, Oxford, 1998.
  11. Il’kiv V.S., Ptashnyk B.I. Problems for partial differential equations with nonlocal conditions. Metric approach to the problem of small denominators. Ukrainian Math. J. 2006, 58 (12), 1847–1875. doi:10.1007/s11253-006-0172-8 (translation of Ukrain. Mat. Zh. 2006, 58 (12), 1624–1650. (in Ukrainian))
  12. Jovanovic B.S., Vulkov L.G. Analysis and numerical approximation of a parabolic-hyperbolic transmission problem. Centr. Eur. J. Math. 2012, 10 (1), 73–84. doi:10.2478/s11533-011-0114-z
  13. Kapustyan V.O., Pyshnograev I.O. Conditions for the existence and uniqueness of the solution of a parabolic-hyperbolic equation with nonlocal boundary conditions. Naukovi Visti 2012, 4 (84), 72–76. (in Ukrainian)
  14. Khinchin A. Continued fractions. Dover Publications, Inc., Mineola, 1997.
  15. Kuz A.M., Ptashnyk B.Yo. A problem with condition containing an integral term for a parabolic-hyperbolic equation. Ukr. Math. J. 2015, 67 (5), 723–734. doi:10.1007/s11253-015-1110-4 (translation of Ukrain. Mat. Zh. 2015, 67 (5), 635–644. (in Ukrainian))
  16. Milovanovic Z. Parabolic-hyperbolic transmission problem in disjoint domains. Filomat 2018, 32 (20), 6911–6920. doi:10.2298/FIL1820911M
  17. Ptashnyk B.Yo., Il’kiv V.S., Kmit’ I.Ya., Polishchuk V.M. Nonlocal boundary value problems for partial differential equations. Naukova Dumka, Kyiv, 2002. (in Ukrainian)
  18. Rassias J. M. Mixed-type partial differential equations with initial and boundary values in fluid mechanics. Int. J. Appl. Math. Statist. 2008, 13 (J08), 77–107.
  19. Roth K.F. Rational approximations to algebraic numbers. Mathematika 1955, 2 (1), 1–20. doi:10.1112/S0025579300000644
  20. Sauer T. Continued fractions and signal processing. Springer, Cham, 2021.
  21. Savka I., Tymkiv I. Problem of linear conjugation with multipoint conditions in the case of multiple nodes for higher-order strictly hyperbolic homogeneous equations. J Math. Sci. 2024, 282, 718–734. doi:10.1007/s10958-024-07211-z