Evolutionary weighted p-Laplacian with boundary degeneracy☆
Evolutionary weighted p-Laplacian with boundary degeneracy☆
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DOI：
10.1016/j.jde.2007.03.012
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发表时间：
2007-06
影响因子：
2.4
通讯作者：
Jingxue Yin;Chunpeng Wang
中科院分区：
文献类型：
--
作者：
Jingxue Yin;Chunpeng Wang
研究了一类具边界退化的演化加权p-Laplace算子的适定性问题。与经典的线性方程理论不同，本文证明了边界退化部分应分解为两部分：强退化边界和弱退化边界，在强退化边界上方程具有双曲型特征，在弱退化边界上方程仍具有抛物型特征。合理地构造了边值条件，建立了边值问题解的存在唯一性定理。
The paper concerns the well-posedness problem of an evolutionary weighted p-Laplacian with boundary degeneracy. Different from the classical theory for linear equations, it is shown that the degenerate portion of the boundary should be decomposed into two parts: the strongly degenerate boundary on which the equation exhibits hyperbolic characteristics and the weakly degenerate boundary on which the equation still exhibits parabolic characteristics. We formulate reasonably the boundary value condition and establish the existence and uniqueness theorems.