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

Existence of solutions to nonlinear parabolic equations via majorant integral kernel