一类非线性退化抛物型方程最大解的支集不变性  

Invariance in Time of Support of the Maximal Solution for a Nonlinear Degenerate Parabolic Equation

作　　者：魏晓丹[1] 周文书[2] 

机构地区：[1]大连民族学院计算机科学与工程学院,辽宁大连116605 [2]大连民族学院理学院,辽宁大连116605

出　　处：《大连民族学院学报》2009年第1期43-44,共2页Journal of Dalian Nationalities University

摘　　要：研究了一类退化抛物型方程的初边值问题,即非负最大解的局部化性质。通过构造适当的闸函数,并借助于比较原理,证明了最大解的支集关于时间是不变的。研究这种性质的重要意义在于:当用这种模型进行图像处理时,能够很好地保持图像的边界,从而使图像边界附近的去噪效果达到最佳。The localization of solutions for a localization of nonnegative maximal solution. degenerate parabolic equation is studied, eg. the By constructing an appropriate test function and in terms of the comparison theorem, it is shown that the support of the nonnegative maximal solution is unchanged in time. The significance of studying the property is that the boundary of image may be kept well when one uses the model in image processing, and hence a sharp effect for removing noise can be arrived near the boundary of the image.

关 键 词：退化抛物方程 弱解 局部化 支集不变性 

分 类 号：O175.26[理学—数学]