A parabolic bipolynomial fractional Dirichlet-Laplace problem
Texas State University, Department of Mathematics
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.
Parabolic equation, Fractional Dirichlet-Laplace operator, Existence of solutions
Idczak, D. (2022). A parabolic bipolynomial fractional Dirichlet-Laplace problem. <i>Electronic Journal of Differential Equations, 2022</i>(56), pp. 1-20.
Attribution 4.0 International