论文标题
较高的定期估计值在热方程附近的多孔培养基方程
Higher regularity estimates for the porous medium equation near the Heat equation
论文作者
论文摘要
在本文中，我们研究了非线性抛物线方程解决方案$$ u_t =ΔU^m，\ quad m> 1 $$通常称为多孔培养基方程的规律性方面。更确切地说，当方程普遍接近热方程时，我们为沿自由边界$ \ partial \ {u> 0 \} $的有界非负弱解决方案提供了尖锐的规律性估计。结果，在这种情况下还建立了当地的Lipschitz估计。
In this paper we investigate regularity aspects for solutions of the nonlinear parabolic equation $$ u_t= Δu^m, \quad m > 1 $$ usually called the porous medium equation. More precisely, we provide sharp regularity estimates for bounded nonnegative weak solutions along the free boundary $\partial\{u>0\}$, when the equation is universally close to the heat equation. As a consequence, local Lipschitz estimates are also established for this scenario.
