Reverse parabolic equation with integral condition is considered. Well-posedness of reverse parabolic problem in the Hölder space is proved. Coercive stability estimates for solution of three boundary value problems (BVPs) to reverse parabolic equation with integral condition are established.
[1] A. Ashyralyev On the problemof determining the parameter of a parabolic equation Ukrainian Mathematical Journal 62(9) (2011) 1397-1408.
[2] A. Ashyralyev A. Hanalyev and P. E. Sobolevskii Coercive solvability of the nonlocal boundary value problem for parabolic differential equations Abstract and Applied Analysis 6(1) (2001) 53-61.
[3] A. Ashyralyev and P. E. SobolevskiiWell-Posedness of Parabolic Difference Equations Birkhäuser Basel 1994.
[4] A. Ashyralyev and P. E. Sobolevskii New Difference Schemes for Partial Differential Equations Operator Theory Advances and Applications Birkhäuser Verlag Basel Boston Berlin 2004.
[5] A. Ashyralyev A. Dural and Y. Sozen Multipoint nonlocal boundary value problems for reverse parabolic equations: well-posedness Vestnik of Odessa National University: Mathematics and Mechanics 13 (2008) 1-12.
[6] C. Ashyralyyev A. Dural and Y.Sozen Finite difference method for the reverse parabolic problem Abstr. Appl. Anal. 2012 (2012) 1-17.
[7] C.Ashyralyyev and O.Demirdag The difference problem of obtaining the parameter of a parabolic equation Abstr. Appl. Anal. 2012 (2012) 1-14.
[8] C. Ashyralyyev A. Dural and Y. Sozen Finite difference method for the reverse parabolic problem with Neumann condition AIP Conference Proceedings 1470 (2012) 102-105.
[9] M. Dehghan Determination of a control parameter in the two-dimensional diffusion equation Appl. Numer. Math. 37(4) (2001) 489-502.
[10] Y. S. Eidel’man An inverse problem for an evolution equation Mathematical Notes 49(5) (1991) 535-540.
[11] M. Kirane Salman A. Malik and M. A. Al-Gwaiz An inverse source problem for a two dimensional time fractional diffusion equation with nonlocal boundary conditions Mathematical Methods in the Applied Sciences 36(9) (2013) 56-69.
[12] S. I. Kabanikhin Inverse and Ill-posed Problems: Theory and Applications Walter de Gruyter Berlin 2011.
[13] S. G. Krein Linear Differential Equations in Banach Space Nauka Moscow 1966.
[14] I. Orazov and M. A. Sadybekov On a class of problems of determining the temperature and density of heat sources given initial and final temperature Siberian Math. J. 53 (2012) 146-151.
[15] Q. V. Tran M. Kirane H. T. Nguyen and V. T. Nguyen Analysis and numerical simulation of the three-dimensional Cauchy problem for quasi-linear elliptic equations Journal of Mathematical Analysis and Applications 446(1) (2017) 470-492.