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We prove existence of a bounded weak solution to a degenerate quasilinearsubdiffusion problem with bounded measurable coefficients that may explicitlydepend on time. The kernel in the involved integro-differential operator w.r.t.time belongs to the large class of ${\cal PC}$ kernels. In particular, the caseof a fractional time derivative of order less than 1 is included. A keyingredient in the proof is a new compactness criterion of Aubin-Lions typewhich involves function spaces defined in terms of the integro-differentialoperator in time. Boundedness of the solution is obtained by the De Giorgiiteration technique. Sufficiently regular solutions are shown to be unique bymeans of an $L_1$-contraction estimate.

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