Electron. J. Differential Equations, Vol. 2022 (2022), No. 56, pp. 120.
A parabolic bipolynomial fractional DirichletLaplace problem
Dariusz Idczak
Abstract:
We derive existence results for a parabolic bipolynomial abstract and
classical problems containing fractional powers of the DirichletLaplace operator
on a bounded domain, in the sense of the Stonevon 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 DirichletLaplace operator;
existence of solutions.
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Dariusz Idczak
Faculty of Mathematics and Computer Science
University of Lodz
Banacha 22, 90238 Lodz, Poland
email: dariusz.idczak@wmii.uni.lodz.pl

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