Minimax estimation with incomplete data of the solution of the initial-boundary-value Dirichlet problem for the heat equation based on its mixed variational formulation

Gorbatenko Mykola Yuriyovych; Podlipenko Yuriy Kostyantynovich

Gorbatenko Mykola Yuriyovych ¹ , Podlipenko Yuriy Kostyantynovich ²

¹ Department of Mathematical Modeling, Yuriy Fedkovych Chernivtsi National University, Chernivtsi, 58000, Ukraine

² Chernivtsi National University named after Yuriy Fedkovych, Chernivtsi, 58002, Ukraine

Keywords: minimax estimation, the initial-boundary-value Dirichlet problem

Download

Abstract

We obtain a new class of systems of variational equations via whose solutions the minimax estimates of functionals from unknown solutions to the initial boundary value problem for the heat equations are expressed.

References

[1] Nakonechny A.G. Minimax estimation of functionals of solutions of variational equations in Hilbert spaces. - Kyiv: KSU, 1985. - 82 p.

[2] Nakonechny A.G. Optimal control and estimation in partial differential equations. Kyiv: "VPC" Kyiv University, 2004. - 103 p.

[3] Podlipenko Yu. K., Horbatenko M. Yu. Estimation of generalized solutions of linear elliptic equations that admit mixed variational formulation. - Bulletin of the Kyiv University, Series: Physical and Mathematical Sciences, 2008, Nº 3. - P. 158-164.

[4] Cessenat M. Mathematical methods in electromagnetism. Linear theory and applications. World Scientific, Singapore, New Jersey, London, Hong Kong, 1996. - 376 p.

[5] Tema R. Navier-Stokes equations. Theory and numerical analysis. - M.: Mir, 1981. - 408 p.

[6] Thomee V. Galerkin Finite Element Methods for Parabolic Problems. - Springer, 2006. - 370 c.

[7] Boffi D., Gastaldi L. Analysis of finite element approximation of evolution problems in mixed form, SIAM J. Numer. Anal., 42 (2004), pp. 1502 -1526.

Download

Cite

ACS Style: Gorbatenko, M.Y.; Podlipenko, Y.K. Minimax estimation with incomplete data of the solution of the initial-boundary-value Dirichlet problem for the heat equation based on its mixed variational formulation. Bukovinian Mathematical Journal. 2018, 1
AMA Style: Gorbatenko MY, Podlipenko YK. Minimax estimation with incomplete data of the solution of the initial-boundary-value Dirichlet problem for the heat equation based on its mixed variational formulation. Bukovinian Mathematical Journal. 2018; 1(528 ).
Chicago/Turabian Style: Mykola Yuriyovych Gorbatenko, Yuriy Kostyantynovich Podlipenko. 2018. "Minimax estimation with incomplete data of the solution of the initial-boundary-value Dirichlet problem for the heat equation based on its mixed variational formulation". Bukovinian Mathematical Journal. 1 no. 528 .

Export

BibTex EndNote RIS