Interior Boundary Value Problem for a System of Second-Order Mixed-Type Equations
DOI:
https://doi.org/10.71310/pcam.5_69.2025.07Keywords:
ill-posed problem, mixed type, inverse problem, uniqueness, system of equationsAbstract
Mathematical models of many applied problems lead to the need to solve interiorboundary value problems for partial differential equations. The problem under study belongs to the class of ill-posed problems in mathematical physics. The issue of small denominators arises; the existence and uniqueness of the solution depend on the numerical properties of the problem data. Theorems on the uniqueness of the solution and its conditional stability on the well-posedness set are proven, a priori estimates for the solution are obtained, and approximate solutions are constructed using the regularization method. The development of approximate methods for their solution is based on the construction and analysis of numerical methods for solving problems with interior and boundary data for the basic (fundamental, model) equations of mathematical physics.
References
Fayazov K.S., Abdullayeva Z.Sh. An interior boundary value problem for a system of partial differential equations of mixed type // Problems of Computational and Applied Mathematics. – 2021. – No. 6/1(37). – P. 29-43.
Fayazov K.S., Abdullayeva Z.Sh. Conditional Correctness of the Internal Boundary Value Problem of the Pseudoparabolic Equation with a Changing Time Direction // Missouri J. Math. Sci. – 2020. – No. 32. – P. 49-60. – doi: http://dx.doi.org/10.35834/2020/3201049.
Pyatkov S.G. Properties of eigen functions of a spectral problem and some of their applications // Some Applications of Functional Analysis to Problems of Mathematical Physics. – Novosibirsk, 1986. – P. 65-84.
Ptashnik B.I. Ill-posed boundary value problems for differential equations with partial derivatives. – Kiev: Naukova dumka, 1984. – 264 p.
Fayazov K.S., Khazhiyev I.O. Uslovnaya ustoychivost' krayevoy zadachi dlya sistemy abstraktnykh differentsial'nykh uravneniy vtorogo poryadka s operatornymi koeffitsiyentami // Uzbek Mathematical Journal. – 2017. – No. 2. – C. 145-155.
Fayazov K.S. The incorrect Cauchy problem for a first order and second-order differential equation with operator coefficients // Siberian Mathematical Journal. – 1994. – Vol. 35, No. 3. – P. 702-706.
Sabitov K.B., Safin E.M. Obratnaya zadacha dlya uravneniya smeshannogo parabolo-giperbolicheskogo tipa // Matematicheskiye zametki. – No. 6. – 2010. – S. 907-918.
Sabitov K.B., Safin E.M. Obratnaya zadacha dlya uravneniya smeshannogo parabolo-giperbolicheskogo tipa v pryamougol'noy oblasti // Izvestiya vuzov. Matematika. – 2010. – No. 4. – S. 55-62.
Fayazov K.S., Abdullayeva Z.SH. Zadacha s vnutrennimi i granichnymi dannymi dlya differentsial'no-operatornogo uravneniya n-go poryadka // Uzbekskiy matematicheskiy zhurnal. – 2014. – No. 2/1. – S. 55-62.
Fayazov K.S., Abdullayeva Z.SH. Mnogotochechnaya zadacha dlya differentsial'nogo uravneniya smeshannogo tipa chetvertogo poryadka // Uzbekskiy matematicheskiy zhurnal. – No. 3. – S. 125-135.
Fayazov K.S., Abdullayeva Z.SH. Vnutrennyaya krayevaya zadacha dlya uravneniya v chastnykh proizvodnykh tret'yego poryadka sostavnogo tipa // Problemy vychislitel'noy i prikladnoy matematiki. – 2017. – No. 4. – S. 68-75.
Downloads
Published
Issue
Section
License
Copyright (c) 2025 K.S. Fayazov
This work is licensed under a Creative Commons Attribution 4.0 International License.
