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Volume 4, Issue 2
Some Properties of Free Boundary for Solution of Porous Medium Equation with Gravity Term in One-dimension

Lu Guofu

J. Part. Diff. Eq.,4(1991),pp.19-35

Published online: 1991-04

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  • Abstract
Consider the degenerate parabolic equation (porous medium equation with gravity term): u_t = (u^m)_{xx} + (u^n)_x, -∞ < x < ∞, t > 0, m > 1 u(x, 0) = u_0(x), -∞ < x < ∞ The main results consist of the estimation of t^∗_i called waiting time, the behavior of pressure V = \frac{m}{m-1}u^{m-1} near a vertical or a nonvertical part of ς_i(t) and a condition of that ς_i(t) is continuously differentiable.
  • Keywords

porous medium equation gravity term free boundary C&sup1 regularity waiting time

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@Article{JPDE-4-19, author = {Lu Guofu}, title = {Some Properties of Free Boundary for Solution of Porous Medium Equation with Gravity Term in One-dimension}, journal = {Journal of Partial Differential Equations}, year = {1991}, volume = {4}, number = {2}, pages = {19--35}, abstract = { Consider the degenerate parabolic equation (porous medium equation with gravity term): u_t = (u^m)_{xx} + (u^n)_x, -∞ < x < ∞, t > 0, m > 1 u(x, 0) = u_0(x), -∞ < x < ∞ The main results consist of the estimation of t^∗_i called waiting time, the behavior of pressure V = \frac{m}{m-1}u^{m-1} near a vertical or a nonvertical part of ς_i(t) and a condition of that ς_i(t) is continuously differentiable.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5765.html} }
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 - C¹ regularity KW - waiting time AB - Consider the degenerate parabolic equation (porous medium equation with gravity term): u_t = (u^m)_{xx} + (u^n)_x, -∞ < x < ∞, t > 0, m > 1 u(x, 0) = u_0(x), -∞ < x < ∞ The main results consist of the estimation of t^∗_i called waiting time, the behavior of pressure V = \frac{m}{m-1}u^{m-1} near a vertical or a nonvertical part of ς_i(t) and a condition of that ς_i(t) is continuously differentiable.
Lu Guofu. (1991). Some Properties of Free Boundary for Solution of Porous Medium Equation with Gravity Term in One-dimension. Journal of Partial Differential Equations. 4 (2). 19-35. doi:
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