najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2017-8-4-413-419najo-588Research ArticleMATHEMATICSМАТЕМАТИКАThe loaded parabolic-hyperbolic equation and its relation to non-local problemsThe loaded parabolic-hyperbolic equation and its relation to non-local problemsBaltaevaU. I.BaltaevaU. I.

department of Differential equations and Mathematical physics

100174; Tashkent

department of Differential equations and Mathematical physics

100174; Tashkent

umidabaltayeva@mail.ruNational University of Uzbekistan named after Mirzo UlugbekNational University of Uzbekistan named after Mirzo Ulugbek20171308202584413419Copyright © Baltaeva U.I., 20252025Baltaeva U.I.Baltaeva U.I.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/588

   In this present paper, unique solvability is proved for the boundary value problems for the loaded differential equations associated with non-local boundary value problems, for the classical partial differential equations.

   In this present paper, unique solvability is proved for the boundary value problems for the loaded differential equations associated with non-local boundary value problems, for the classical partial differential equations.

parabolic-hyperbolic type equationsnon-local problemsloaded equationboundary value problemsgluing conditionintegral equationparabolic-hyperbolic type equationsnon-local problemsloaded equationboundary value problemsgluing conditionintegral equationReferencesNakhushev A.M. Loaded equations and their applications, Differential equations, 1983, 19(1), P. 86–94.Nakhushev A.M. Loaded equations and their applications, Differential equations, 1983, 19(1), P. 86–94.Wiener J., Debnath L. Partial differential equations with piecewise constant delay, Internat. J. Math. and Math. Scz., 1991, 14, P. 485-496.Wiener J., Debnath L. Partial differential equations with piecewise constant delay, Internat. J. Math. and Math. Scz., 1991, 14, P. 485-496.Dzhenaliev M.T. A remark on the theory of linear boundary value problems for loaded differential equations. Almaty, Institute of Theoretical and Applied Mathematics, 1995, 270 p.Dzhenaliev M.T. A remark on the theory of linear boundary value problems for loaded differential equations. Almaty, Institute of Theoretical and Applied Mathematics, 1995, 270 p.Nakhushev A.M. Equations of mathematical biology. Vishaya shkola, Moscow, 1995, 302 p.Nakhushev A.M. Equations of mathematical biology. Vishaya shkola, Moscow, 1995, 302 p.Baltaeva U.I. Solvability of the analogs of the problem Tricomi for the mixed type loaded equations with parabolic-hyperbolic operators. Boundary Value Problems, 2014, 21, P. 1–12.Baltaeva U.I. Solvability of the analogs of the problem Tricomi for the mixed type loaded equations with parabolic-hyperbolic operators. Boundary Value Problems, 2014, 21, P. 1–12.Nakhushev A.M. Nonlocal problem and the Goursat problem for loaded hyperbolic equation and their application in prediction of ground moisture. Soviet Math. Dokl., 1978, 19(5), P. 1243–1247.Nakhushev A.M. Nonlocal problem and the Goursat problem for loaded hyperbolic equation and their application in prediction of ground moisture. Soviet Math. Dokl., 1978, 19(5), P. 1243–1247.Kirillova S.A., Almjashev V.I., Gusarov V.V. Spinodal decomposition in the SiOsub>2</sub>-TiOsub>2</sub> system and hierarchically organized nanostructures formation. Nanosystems: Phys. Chem. Math., 2012, 3(2), P. 100–115.Kirillova S.A., Almjashev V.I., Gusarov V.V. Spinodal decomposition in the SiOsub>2</sub>-TiOsub>2</sub> system and hierarchically organized nanostructures formation. Nanosystems: Phys. Chem. Math., 2012, 3(2), P. 100–115.Antonov N.M., Popov I.Yu., Gusarov V.V. Model of spinodal decomposition of phases under hyperbolic diffusion. Physics of the Solid State, 1999, 41(5), P. 824–826.Antonov N.M., Popov I.Yu., Gusarov V.V. Model of spinodal decomposition of phases under hyperbolic diffusion. Physics of the Solid State, 1999, 41(5), P. 824–826.Melikhov I.F. Asymptotic solution of ultrasonic near-field levitation problem. Nanosystems: Phys. Chem. Math., 2017, 8(2), P. 260–265.Melikhov I.F. Asymptotic solution of ultrasonic near-field levitation problem. Nanosystems: Phys. Chem. Math., 2017, 8(2), P. 260–265.Islomov B.I., Baltaeva U.I. Boundary value problems for the loaded equations of the hyperbolic and mixed types. Ufa mathematical journal, 2011, 3(3), P. 15–25.Islomov B.I., Baltaeva U.I. Boundary value problems for the loaded equations of the hyperbolic and mixed types. Ufa mathematical journal, 2011, 3(3), P. 15–25.Krasnov M.L. Integral equations. Introduction to the theory. Moscow, Nauka, 1975.Krasnov M.L. Integral equations. Introduction to the theory. Moscow, Nauka, 1975.Dzhurayev T.D., Sopuev A. and Mamayhonov M. Boundary value problems for the problems for the parabolic-hyperbolic type equations. Tashkent, Fan, 1986.Dzhurayev T.D., Sopuev A. and Mamayhonov M. Boundary value problems for the problems for the parabolic-hyperbolic type equations. Tashkent, Fan, 1986.Sabytov K.B. To the theory of mixed parabolic-hyperbolic type equations with a spectral parameter, Differential equations, 1989, 25(1), P. 117–126.Sabytov K.B. To the theory of mixed parabolic-hyperbolic type equations with a spectral parameter, Differential equations, 1989, 25(1), P. 117–126.Salakhitdinov M.S., Urinov A.K. Boundary value problems for equations of mixed type with a spectral parameter. Tashkent, Fan, 1997.Salakhitdinov M.S., Urinov A.K. Boundary value problems for equations of mixed type with a spectral parameter. Tashkent, Fan, 1997.Berdyshev A.S. Non-local boundary value problems for the mixed type equation in a domain with deviation from a characteristic. Differential equations, 1993, 29(12), P. 2118–2125.Berdyshev A.S. Non-local boundary value problems for the mixed type equation in a domain with deviation from a characteristic. Differential equations, 1993, 29(12), P. 2118–2125.Serbina L.I. Nonlocal mathematical models of transport processes in systems with a fractal structure. Nal’chik, 2002, 144 p.Serbina L.I. Nonlocal mathematical models of transport processes in systems with a fractal structure. Nal’chik, 2002, 144 p.Berdyshev A.S., Karimov E.T. Some non-local problems for the parabolic-hyperbolic type equation with non-characteristic line of changing type. Differential equations, 2006, 4(2), P. 183–193.Berdyshev A.S., Karimov E.T. Some non-local problems for the parabolic-hyperbolic type equation with non-characteristic line of changing type. Differential equations, 2006, 4(2), P. 183–193.Kishin B. Sadarangani, Abdullaev Obidjon Kh. About a problem for loaded parabolic-hyperbolic type equation with fractional derivatives. International Journal of Differential equations, Volume 2016, Article ID 9815796, 6 p.Kishin B. Sadarangani, Abdullaev Obidjon Kh. About a problem for loaded parabolic-hyperbolic type equation with fractional derivatives. International Journal of Differential equations, Volume 2016, Article ID 9815796, 6 p.Tikhonov A.N., Samarskij A.A. Equations of Mathematical Physics. Nauka, Moscow, 1966.Tikhonov A.N., Samarskij A.A. Equations of Mathematical Physics. Nauka, Moscow, 1966.

The authors declare that there are no conflicts of interest present.