The seminar will cover the subject matter of continuous dependency of mild solutions of linear PDEs of parabolic type with time varying delay with respect to: initial data, parameters and delay jointly. The main equation is complemented with boundary conditions of Dirichlet, Neumann or Robin type. The seminar will present the sufficient assumptions on the initial condition, coefficients, and delay map that can be assumed to obtain continuous dependence in suitable topology of coefficient space. These results have application in mathematical ecology to model dependencies between species, especially species extinction.

