Determine the spacial term of a two-dimensional heat source

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

We consider the problem of determining a pair of functions $(u,f)$ satisfying the heat equation $u_t-\Delta u=\phi (t)f(x,y)$, where $(x,y)\in \Omega =(0,1)\times (0,1)$ and the function $\phi$ is…