Existence of solutions for a higher-order semilinear parabolic equation with singular initial data
Shinya Okabe, Kazuhiro Ishige, Tatsuki Kawakami
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.
Topics & Concepts
MathematicsSingularityInitial value problemKernel (algebra)Cauchy problemOrder (exchange)Mathematical analysisParabolic partial differential equationCauchy distributionApplied mathematicsPure mathematicsPartial differential equationEconomicsFinanceAdvanced Mathematical Physics ProblemsStability and Controllability of Differential EquationsNonlinear Partial Differential Equations