In this paper, we investigate the long-term behavior for an invariant plane curve flow, whose evolution process can be expressed as a second-order nonlinear parabolic equation with respect to centro-affine curvature. The forward and backward limits in time are discussed, which shows that closed convex embedded may converge ellipse when evolving according flow. addition, obtain isoperimetric ine...

This paper concerns with the asymptotic behavior of complete non-compact convex curves embedded in $\Bbb{R}^2$ under $\alpha$-curve shortening flow for exponents $\alpha>{1\over 2}$. We show that any such curve having addition its two ends to parallel lines, converges unique translating soliton whose are same lines. is a new result even standard case $\alpha=1$, and we prove all up critical

Wax deposition phenomenon changes the rheological behavior of waxy crude oil completely. In the current work, the rheological time-dependent and time-independent behaviors of waxy crude oil samples are studied and flow curve and compliance function are measured for the oil samples with various wax contents at different temperatures. A decrease in temperature and an increase in wax content lead ...