Existence of solutions for a higher-order semilinear parabolic equation with singular initial data (1909.05492v1)

Published 12 Sep 2019 in math.AP

Abstract: We establish the existence of solutions of the Cauchy problem for a higher-order semilinear parabolic equation by introducing a new majorizing kernel. We also study necessary conditions on the initial data for the existence of local-in-time solutions and identify the strongest singularity of the initial data for the solvability of the Cauchy problem.

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