Bounded weak solutions of time-fractional porous medium type and more general nonlinear and degenerate evolutionary integro-differential equations

We prove existence of a bounded weak solution to degenerate quasilinear subdiffusion problem with measurable coefficients that may explicitly depend on time. The kernel in the involved integro-differential operator w.r.t. time belongs large class PC kernels. In particular, case fractional derivative order less than 1 is included. A key ingredient proof new compactness criterion Aubin-Lions type which involves function spaces defined terms Boundedness obtained by De Giorgi iteration technique. Sufficiently regular solutions are shown be unique means an L1-contraction estimate.