Initial traces of solutions to a semilinear heat equation under the Dirichlet boundary condition

We study qualitative properties of initial traces of nonnegative solutions to a semilinear heat equation in a smooth domain under the Dirichlet boundary condition. Furthermore, for the corresponding Cauchy–Dirichlet problem, we obtain sharp necessary conditions and sufficient conditions on the existence of nonnegative solutions and identify optimal singularities of solvable nonnegative initial data.