Inverse problem for semilinear Eidelman type equation

N.P. Protsakh; O. E.  Parasiuk-Zasun

doi:10.30970/ms.53.1.48-58

N.P. Protsakh Ukrainian National Forestry University, Lviv, Ukraine
O. E. Parasiuk-Zasun Diablo Valley College San Ramon Campus, San Ramon, USA Chabot College Hesperian Blvd Hayward, USA

DOI: https://doi.org/10.30970/ms.53.1.48-58

Анотація

The inverse problem for semilinear Eidelman type equation with unknown time dependent function in its right-hand side is considered in this paper. The initial, boundary and integral type overdetermination conditions are posed. The sufficient conditions of the existence and the uniqueness of weak solution for the problem are obtained.

Посилання

O.E. Korkuna, S.P. Lavrenyuk, A mixed problem for one nonlinear Eidelman equation in an unbounded domain, Reports of the NAS of Ukraine. – 2008. – No4. – P. 24–30.

O.E. Korkuna, Mixed problem for nonlinear Eidelman equation with integral term, Carpathian Math. Publ. – 2012. – V.4, No2. – P. 275–283.

S.D. Eidelman, On a class of parabolic systems, Reports of AS SSSR. – 1960. – V.133, No1. – P. 40–43.

S.D. Eidelman, S.D. Ivasyshen, A.N. Kochubei, Analytic methods in the theory of differential and pseudo-differential equations of parabolic type, Birkhäuser Verlag, 2004, 390 p.

S.D. Ivasyshen, I.P. Medynsky, On applications of the Levi method in the theory of parabolic equations, Mat. Stud. – 2017. – V.47, No1. – P. 33–46.

H. Torhan, Mixed problem for Eidelman type evolution equation in unbounded region, Visnyk of the Lviv University. Series Mechanics and Mathematics. – 2007. – V.67. – P. 248–267.

M.I. Ivanchov, Inverse problems for equations of parabolic type, Mathematical Studies, Monograph Series, VNTL Publishers, 2003, V.10, 238p.

A. Lopushanskyy, H. Lopushanska, Inverse problem for 2b-order differential equation with a time-fractional derivative, Carpathian Math. Publ. – 2019. – V.11, No1. – P. 107–118.

V.L. Kamynin, On the inverse problem of determining the right-hand side of a parabolic equation under an integral overdetermination condition, Mathematical Notes. – 2005. – V.77, No4. – P. 482–493.

A.I. Prilepko, V.L. Kamynin, A.B. Kostin, Inverse source problem for parabolic equation with the condition of integral observation in time, Computational Mathematics and Mathematical Physics. – 2017. – V.57, No6. – P. 956–966.

S.G. Pyatkov, E.I. Safonov, Determination of the source function in mathematical models of convection-diffusion, Mat. Zametki Severo-Vost. Fed. Univ. – 2014.– V.21, No2. – P. 117–130.

V.T. Borukhov, P.N. Vabishchevich, Numerical solution of the inverse problem of recovering a distributed right-hand side of a parabolic equation, Computer Physics Communications. – 2000. – V.126, P. 32–36.

N.P. Protsakh, B.Yo. Ptashnyk, Nonlinear ultraparabolic equations and variational inequalities, “Naukova dumka”, Kyiv, 2017, 278 p.

N. Protsakh, Determining of right-hand side of higher order ultraparabolic equation, Open Math. – 2017. – V.15. – P. 1048–1062.

N.P. Protsakh, Problem of determining of minor coefficient and right-hand side function in semilinear ultraparabolic equation, Mat. Stud. – 2018. – V.50, No21. – P. 60–74.