Local boundedness for solutions to degenerate parabolic double phase problems

In this paper, we investigate the local boundedness of weak solutions to degenerate parabolic double phase equation of type $$u_t-\text{div}(\mathrm{\mid }Du{\mathrm{\mid }}^{p-2}Du+a(x,t)\mathrm{\mid }Du{\mathrm{\mid }}^{q-2}Du)=0\text{in }{\mathrm{\Omega }}_T:=\mathrm{\Omega }\times (0,T),$$ where $0\le a(\cdot )\in L^{\mathrm{\infty }}({\mathrm{\Omega }}_T)$. To this end, we derive the Caccioppoli inequality and a parabolic embedding theorem, which are then utilized in an iteration method.