A new approach to initial traces in nonlinear filtration
A new approach to initial traces in nonlinear filtration
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DOI：
10.1016/s0294-1449(16)30294-3
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发表时间：
1990-07
影响因子：
1.9
通讯作者：
D. Andreucci;E. D. Benedetto
中科院分区：
文献类型：
--
作者：
D. Andreucci;E. D. Benedetto
对于非线性滤波型方程inrnx (0， T), 0 < T <∞的弱解，我们证明了精确超估计和局部和全局Harnack型不等式。这些估计允许识别初始轨迹并描述|x|→∞等解的行为。重点是引入一种新的方法，摆脱了多孔介质方程的均匀性、标度、拟凸性等特征。这种方法一方面可以推广到各种各样的方程，另一方面在梯度平均上产生新的结果。
For weak solutions of equations of the type of nonlinear filtration inRN× (0, T), 0 < T < ∞, we prove precise sup-estimates and local and global Harnack type inequalities. These estimations permit to identify the initial traces and describe the behavior of such solutions as |x| → ∞.The main point is to introduce a new approach, free of the specific features of the porous medium equation such as homogeneity, scaling, quasi-convexity, etc. This approach on one hand allows generalizations to a large variety of equations and on other yields new results on gradient averages.