  We establish the existence of solutions to the Cauchy problem for a large
class of nonlinear parabolic equations including fractional semilinear
parabolic equations, higher-order semilinear parabolic equations, and viscous
Hamilton-Jacobi equations by using the majorant kernel introduced in [K.
Ishige, T. Kawakami, and S. Okabe, Ann. Inst. H. Poincar\'e Anal. Non
Lin\'eaire 37 (2020), 1185--1209].
