An inverse backward problem for degenerate two-dimensional parabolic equation

This paper deals with the determination of an initial condition in the degenerate two-dimensional parabolic equation \[\partial_{t}u-\mathrm{div}\left(a(x,y)I_2\nabla u\right)=f,\quad (x,y)\in\Omega,\; t\in(0,T),\] where \(\Omega\) is an open, bounded subset of \(\mathbb{R}^2\), \(a \in C^1(\bar{\Omega})\) with \(a\geqslant 0\) everywhere, and \(f\in L^{2}(\Omega \times (0,T))\), with initial and…