Перейти до основного вмісту
Inverse problem for a parabolic equation with a nonlocal overdetermination condition
Kinash Natalia Evgenivna 1
1 Ivan Franko National University of Lviv, Ivan Franko National University of Lviv, 79000, Ukraine
Keywords: inverse problem, parabolic equation, a nonlocal overdetermination condition
Abstract
An inverse problem for a one-dimensional parabolic equation with unknown time-dependent leading coefficient with a nonlocal overdetermination condition is investigated. The existence and uniqueness conditions of the classical solution to the problem are obtained.
References

[1] Nakhushev A.M. Equations of Mathematical Biology. - M.: Vysh.shk., 1995. - 301 p.

[2] Ivanchov M.I. Inverse problems of heat conduction with nonlocal conditions: Preprint. - K.: ISDO, 1995. - 84 p.

[3]  Ismailov M.I., Kanca F. An inverse coefficient problem for a parabolic equation in the case of nonlocal boundary and overdetermination conditions // Math. Meth. Apl. Sci. – 2011. – 34 . – P. 692–702.

[4]  Lesnic D., Yousefi S.A., Ivanchov M. Determination of a time-dependent diffusivity from nonlocal  conditions // J. Appl. Math. Comput. – 2013. – 41 . – P. 301–320.

[5]  Lukshin A.V., Reznik B.I. Unique solvability of the inverse problem for the heat equation with nonlocal boundary conditions // Appl. Math. Inf. Sci. – 2007. – 18 , N1. – P. 29-41.

[6] Bereznitskaya I.B. Inverse problem for a parabolic equation with a nonlocal redefinition condition (in Russian) // Mat. methods and fiz. mekh. polya. - 2001. - 44, N1. - P. 54-62.

[7] Ladyzhenskaya O.A., Solonnikov V.A., Uraltseva N.N. Linear and quasilinear equations of parabolic type. - M.: Nauka, 1967. - 736 p.

[8] Ivanchov M. Inverse problems for equations of parabolic type // Math. Studies: Monograph Ser. – 2003. – 10 , N1. – 238 p.

[9] Friedman A. Equations with partial derivatives of parabolic type. - M.: Mir, 1967. -428 с.

[10] Bereznitskaya I., Drebot A., Makar Y. Inverse problems for the heat conduction equation with nonlocal and integral conditions // Lviv Univ. Series of Mech.-Mat. - 1999. - 54. - P. 27-37.

[11] Hryntsiv N.M. Nonlocal inverse problems for a weakly degenerate parabolic equation // Newsletter of the National University “Lvivska politechnika”. Physics and Mathematical Sciences. - 2011. - 696 , N696. - С. 32-39.

Cite
ACS Style
Kinash, N.E. Inverse problem for a parabolic equation with a nonlocal overdetermination condition. Bukovinian Mathematical Journal. 2016, 3
AMA Style
Kinash NE. Inverse problem for a parabolic equation with a nonlocal overdetermination condition. Bukovinian Mathematical Journal. 2016; 3(1).
Chicago/Turabian Style
Natalia Evgenivna Kinash. 2016. "Inverse problem for a parabolic equation with a nonlocal overdetermination condition". Bukovinian Mathematical Journal. 3 no. 1.
Export
We use own, third-party cookies, and localStorage files to analyze web traffic and page activities. Privacy Policy Settings