Electron. J. Differential Equations, Vol. 2022 (2022), No. 56, pp. 1-20.

A parabolic bipolynomial fractional Dirichlet-Laplace problem

Dariusz Idczak

We derive existence results for a parabolic bipolynomial abstract and classical problems containing fractional powers of the Dirichlet-Laplace operator on a bounded domain, in the sense of the Stone-von Neumann operator calculus. The main tools are theorems on the existence and uniqueness of a weak solutions to an abstract problem, due to Friedman, and a general theorem on the equivalence of weak and strong solutions to some operator equation.

Submitted December 8, 2021. Published July 31, 2022.
Math Subject Classifications: 35K10, 35R11.
Key Words: Parabolic equation; fractional Dirichlet-Laplace operator; existence of solutions.

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Dariusz Idczak
Faculty of Mathematics and Computer Science
University of Lodz
Banacha 22, 90-238 Lodz, Poland
email: dariusz.idczak@wmii.uni.lodz.pl

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