DETERMINATION OF A TIME - DEPENDENT TERM IN THE RIGHT HAND SIDE OF LINEAR PARABOLIC EQUATIO NS WITH ROBIN BOUNDARY CONDITION FROM BOUNDARY OBSERVATIONS

Bùi Việt Hương

doi:10.34238/tnu-jst.5334

DETERMINATION OF A TIME - DEPENDENT TERM IN THE RIGHT HAND SIDE OF LINEAR PARABOLIC EQUATIO NS WITH ROBIN BOUNDARY CONDITION FROM BOUNDARY OBSERVATIONS

About this article

Received: 08/12/21 Revised: 28/02/22 Published: 28/02/22

Authors

Bui Viet Huong , University of Transport and Communications

Abstract

We propose a variational method for determining a time-dependent term in the right hand side of parabolic equations with Robin boundary condition from boundary observations. We have shown the formula for functional to be minimized gradient via an adjoint problem. The direct problem is discretized by the finite difference methods and the variational problem is solved by the conjugate gradient method and Tikhonov regularization.

Keywords

Inverse problems; Ill-posed problems; Boundary observations; Finite difference methods; Conjugate gradient methods

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DOI: https://doi.org/10.34238/tnu-jst.5334

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