Determine the source term of a two-dimensional heat equation
  Let $\Omega$ be a two-dimensional heat conduction body. We consider the problem of determining the heat source $F(x,t)=\varphi(t)f(x,y)$ with $\varphi$ be given inexactly and $f$ be unknown. The problem is nonlinear and ill-posed. By a specific form of Fourier transforms, we shall show that the heat source is determined uniquely by the minimum boundary condition and the temperature distribution in $\Omega$ at the initial time $t=0$ and at the final time $t=1$. Using the methods of Tikhonov's regularization and truncated integration, we construct the regularized solutions. Numerical part is given. 
Dang Duc Trong (UNS-HCMC), Truong Trung Tuyen (IU), Phan Thanh Nam   (UNS-HCMC), Alain Pham Ngoc Dinh (MAPMO)