Idczak, Dariusz2023-04-252023-04-252022-07-31Idczak, D. (2022). A parabolic bipolynomial fractional Dirichlet-Laplace problem. <i>Electronic Journal of Differential Equations, 2022</i>(56), pp. 1-20.1072-6691https://hdl.handle.net/10877/16646We 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.Text20 pages1 file (.pdf)enAttribution 4.0 InternationalParabolic equationFractional Dirichlet-Laplace operatorExistence of solutionsArticle