Expanding solutions of quasilinear parabolic equations

By using the theory of maximal \begin{document}$ L^{q} $\end{document}-regularity and methods singular analysis, we show a Taylor's type expansion–with respect to geodesic distance around an arbitrary point–for solutions quasilinear parabolic equations on closed manifolds. The powers expansion are determined explicitly by local geometry, whose reflection is established through space asymptotics.