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Existence of solutions for a higher-order semilinear parabolic equation with singular initial data |
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| Institution: | 1. Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia;2. Department of Mathematics and Computer Science, University of Palermo, Via Archirafi 34, 90123, Palermo, Italy |
| 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. |
| Keywords: | Higher-order semilinear parabolic equation Majorizing kernel Singular initial data Solvability |
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