Retrospective continuation of solutions to semilinear parabolic equations (Q1907441)

The semilinear parabolic equation \[ \sum^n_{i, j= 1} {\partial\over \partial x_i} \Biggl(a_{ij}(x){\partial u\over \partial x_j}\Biggr)- {\partial u\over \partial t}= F(x, u) \] is considered. The possibility of stably continuing a solution \(u(x, t)\) to the past \((t< 0)\) is investigated. The solution in a bounded domain \(G\subset \mathbb{R}^n\) at \(t= 0\) is given.