Fractional Burgers equation in a bounded domain
Volume 151 / 2018
Colloquium Mathematicum 151 (2018), 57-70
MSC: Primary 35S11.
DOI: 10.4064/cm7063-2-2017
Published online: 27 October 2017
Abstract
Solvability of Dirichlet’s problem for the subcritical fractional Burgers equation is discussed here in two base spaces: $L^2(I)$ and $H^s(I)$ with $s \gt {1/2}$. A solution in the critical case ($\alpha ={1/2}$) is then obtained as a limit of $X^{{1/(2\alpha )}}$ solutions to the subcritical equations, when the exponent $\alpha $ of $(-\varDelta )^\alpha $ tends to ${1/2}^+$.
