Solvability of Superlinear Fractional Parabolic Equations
Yohei Fujishima, Kotaro Hisa, Kazuhiro Ishige, Robert Laister
TL;DR
This paper investigates the conditions under which solutions exist for superlinear fractional parabolic equations, clarifying how initial singularities influence solvability.
Contribution
It provides sharp necessary and sufficient conditions for local solutions, linking initial measure singularities with equation solvability.
Findings
Established sharp criteria for solution existence
Clarified the role of initial measure singularities
Connected solvability with equation parameters
Abstract
We study necessary conditions and sufficient conditions for the existence of local-in-time solutions of the Cauchy problem for superlinear fractional parabolic equations. Our conditions are sharp and clarify the relationship between the solvability of the Cauchy problem and the strength of the singularities of the initial measure.
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Taxonomy
TopicsNonlinear Differential Equations Analysis · Fractional Differential Equations Solutions · Differential Equations and Boundary Problems