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Fractional Burgers equation in a bounded domain

Volume 151 / 2018

M. B. Kania 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 ${1/2}^+$.

Authors

  • M. B. KaniaInstitute of Mathematics
    University of Silesia in Katowice
    Bankowa 14
    40-007 Katowice, Poland
    e-mail

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