TY - JOUR
T1 - Some Properties of Free Boundary for Solution of Porous Medium Equation with Gravity Term in One-dimension
AU - Lu Guofu
JO - Journal of Partial Differential Equations
VL - 2
SP - 19
EP - 35
PY - 1991
DA - 1991/04
SN - 4
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5765.html
KW - porous medium equation
KW -  gravity term
KW -  free boundary
KW -  C&sup1 regularity
KW -  waiting time
AB -  Consider the degenerate parabolic equation (porous medium equation with gravity term): u_t = (u^m)_{xx} + (u^n)_x, -&#8734 < x < &#8734, t > 0, m > 1 u(x, 0) = u_0(x), -&#8734 < x < &#8734 The main results consist of the estimation of t^&#8727_i called waiting time, the behavior of pressure V = \frac{m}{m-1}u^{m-1} near a vertical or a nonvertical part of &#962_i(t) and a condition of that &#962_i(t) is continuously differentiable.