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Determine the Spacial Term of a Two-dimensional Heat Source by Trong, Dang Duc; Dinh, Alain Pham Ngoc; Nam, Phan Thanh is a scholarly article available to read on EtoBox.

What is Determine the Spacial Term of a Two-dimensional Heat Source about?

We consider the problem of determining a pair of functions $(u,f)$ satisfying the heat equation $u_t -\Delta u =\varphi(t)f (x,y)$, where $(x,y)\in \Omega=(0,1)\times (0,1)$ and the function $\varphi$ is given. The problem is ill-posed. Under a slight condition on $\varphi$, we show that the solution is determined uniquely from some boundary data and the initial temperature. Using the interpolation method and the truncated Fourier series, we construct a regularized solution of the source term $f$ from non-smooth data. The error estimate and numerical experiments are given.

Author

Trong, Dang Duc; Dinh, Alain Pham Ngoc; Nam, Phan Thanh

Published

2008

Language

EN