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We establish the existence of solutions of the Cauchy problem for ahigher-order semilinear parabolic equation by introducing a new majorizingkernel. We also study necessary conditions on the initial data for theexistence of local-in-time solutions and identify the strongest singularity ofthe initial data for the solvability of the Cauchy problem.

Existence of solutions for a higher-order semilinear parabolic equation with singular initial data