JournalszaaVol. 35, No. 3pp. 333–357

Stability for Semilinear Parabolic Problems in L2L_2 and W1,2W^{1,2}

  • Pavel Gurevich

    Freie Universität Berlin, Germany
  • Martin Väth

    Czech Academy of Sciences, Prague, Czech Republic
Stability for Semilinear Parabolic Problems in $L_2$ and $W^{1,2}$ cover
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Abstract

Asymptotic stability is studied for semilinear parabolic problems in L2(Ω)L_2 (\Omega) and interpolation spaces. Some known results about stability in W1,2(Ω)W^{1,2} (\Omega) are improved for semilinear parabolic systems with mixed boundary conditions. The approach is based on Amann’s power extrapolation scales. In the Hilbert space setting, a better understanding of this approach is provided for operators satisfying Kato’s square root problem.

Cite this article

Pavel Gurevich, Martin Väth, Stability for Semilinear Parabolic Problems in L2L_2 and W1,2W^{1,2}. Z. Anal. Anwend. 35 (2016), no. 3, pp. 333–357

DOI 10.4171/ZAA/1568