The Dirichlet problem in an infinite layer for a system of differential equations with shifts
-
Zinovii Nytrebych
und
Ivan Savka
Abstract
In this paper, we study the problem with data on the boundary of the infinite layer
for the system of two differential equations of the second order in the time variable 𝑡 with shifts in the spatial variables
References
[1] L. Bers, Mathematical Aspects of Subsonic and Transonic Gas Dynamics, Surv. Appl. Math. 3, Dover, Mineola, 2016. Suche in Google Scholar
[2] I. O. Bobyk and M. M. Symotyuk, Dirichlet-type problem for partial differential equations with delay argument, Nauk. Visn. Uzhgorod. Univ. Ser. Mat. Inform. 2 (2017), no. 31, 21–27. Suche in Google Scholar
[3] W. K. Hayman and Z. G. Shanidze, Polynomial solutions of partial differential equations, Methods Appl. Anal. 6 (1999), 97–108. 10.4310/MAA.1999.v6.n1.a7Suche in Google Scholar
[4] G. N. Hile and A. Stanoyevitch, Heat polynomial analogues for equations with higher order time derivatives, J. Math. Anal. Appl. 295 (2004), no. 2, 595–610. 10.1016/j.jmaa.2004.03.039Suche in Google Scholar
[5] N. Hohenbichler and J. Ackermann, Computing stable regions in parameter spaces for a class of quasipolynomials, IFAC Proc. 36 (2003), no. 19, 221–226. 10.1016/S1474-6670(17)33329-3Suche in Google Scholar
[6] V. S. Il’kiv, Solvability of the nonlocal problem for systems of partial differential equations with shifts of arguments, Nauk. Visn. Uzhgorod. Univ. Ser. Mat. Inform. 21 (2010), 72–85. Suche in Google Scholar
[7] V. S. Il’kiv, Solvability of the nonlocal problem for linear inhomogeneous partial differential equations with shifts of arguments, Visn. NU Lviv. Politekhn. Fiz.-Mat. Nauky 718 (2011), 46–53. Suche in Google Scholar
[8] A. I. Kozhanov and L. S. Pul’kina, On the Solvability of boundary problems with shift for linear hyperbolic equations, Matem. Zhurn. Inst. Matem. Minobr i Nauki Respubliki Kazakhstan 2 (2010), no. 32, 78–92. Suche in Google Scholar
[9] O. M. Medvid and M. M. Simotyuk, Problem with integral conditions for a linear system of partial differential equations with delay, Matem. Bull. NTSh 4 (2007), 414–427. Suche in Google Scholar
[10] A. M. Nakhushev, Problems with Shift for Partial Differential Equations, Nauka, Moscow, 2006. Suche in Google Scholar
[11] Z. M. Nytrebych, Differential-symbol method of solving the Dirichlet problem in an infinite strip for a system of differential equations with shifts, Ukr. Mat. Visn. 19 (2022), no. 3, 413–425; translation in J. Math. Sci. (N. Y.) 268 (2022), no. 2, 222–232. Suche in Google Scholar
[12] Z. M. Nytrebych and O. M. Malanchuk, The differential-symbol method of solving the problem two-point in time for a nonhomogeneous partial differential equation, J. Math. Sci. 227 (2017), 68–80. 10.1007/s10958-017-3574-2Suche in Google Scholar
[13] Z. Nytrebych and O. Malanchuk, The differential-symbol method of constructing the quasi-polynomial solutions of two-point problem, Demonstr. Math. 52 (2019), no. 1, 88–96. 10.1515/dema-2019-0010Suche in Google Scholar
[14] P. S. Pedersen, A basis for polynomial solutions to systems of linear constant coefficient PDE’s, Adv. Math. 117 (1996), no. 1, 157–163. 10.1006/aima.1996.0005Suche in Google Scholar
[15] O. A. Repin, Boundary-Value Problems with Shift for Hyperbolic and Mixed-Type Equations, House of Samara University, Samara, 1992. Suche in Google Scholar
[16] A. L. Skubachevskii, Elliptic Functional-Differential Equations and Applications, Oper. Theory Adv. Appl. 91, Birkhäuser, Basel, 1997. 10.1007/978-3-0348-9033-5_3Suche in Google Scholar
© 2023 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Additivity of multiplicative (generalized) skew semi-derivations on rings
- On statistical convergence of order α in partial metric spaces
- Generalized derivations over amalgamated algebras along an ideal
- Numerical radii of operator matrices in terms of certain complex combinations of operators
- Centralizing identities involving generalized derivations in prime rings
- Two presentations of a weak type inequality for geometric maximal operators
- Existence and exponential stability of solutions for a Balakrishnan–Taylor quasilinear wave equation with strong damping and localized nonlinear damping
- Identities with generalized derivations on Lie ideals and Banach algebras
- Essential norm of Riemann–Stieltjes operator on weighted Bergman spaces with doubling weights
- Concerning the Nakayama property of a module
- Multiplicity result for a (p(x),q(x))-Laplacian-like system with indefinite weights
- Finite groups in which some particular invariant subgroups are TI-subgroups or subnormal subgroups
- The Dirichlet problem in an infinite layer for a system of differential equations with shifts
- Signless Laplacian spectrum of the cozero-divisor graph of the commutative ring ℤ𝑛
- A new fuzzy approach of vehicle routing problem for disaster-stricken zones
Artikel in diesem Heft
- Frontmatter
- Additivity of multiplicative (generalized) skew semi-derivations on rings
- On statistical convergence of order α in partial metric spaces
- Generalized derivations over amalgamated algebras along an ideal
- Numerical radii of operator matrices in terms of certain complex combinations of operators
- Centralizing identities involving generalized derivations in prime rings
- Two presentations of a weak type inequality for geometric maximal operators
- Existence and exponential stability of solutions for a Balakrishnan–Taylor quasilinear wave equation with strong damping and localized nonlinear damping
- Identities with generalized derivations on Lie ideals and Banach algebras
- Essential norm of Riemann–Stieltjes operator on weighted Bergman spaces with doubling weights
- Concerning the Nakayama property of a module
- Multiplicity result for a (p(x),q(x))-Laplacian-like system with indefinite weights
- Finite groups in which some particular invariant subgroups are TI-subgroups or subnormal subgroups
- The Dirichlet problem in an infinite layer for a system of differential equations with shifts
- Signless Laplacian spectrum of the cozero-divisor graph of the commutative ring ℤ𝑛
- A new fuzzy approach of vehicle routing problem for disaster-stricken zones
