双非线性抛物方程初始迹与Harnack不等式

詹华税

数学学报 ›› 2014, Vol. 57 ›› Issue (3) : 537-558.

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数学学报 ›› 2014, Vol. 57 ›› Issue (3) : 537-558. DOI: 10.12386/A2014sxxb0051
论文

双非线性抛物方程初始迹与Harnack不等式

    詹华税1,2
作者信息 +

The Initial Trace and the Harnack Inequality of Doubly Nonlinear Parabolic Equations

    Hua Shui ZHAN1,2
Author information +
文章历史 +

摘要

在最优的初始值条件下考虑如下拟线性抛物方程的柯西问题ut-div ax, t,u, Du)=b(x,t, u, Du),(x,t)属于 ST=RN×(0,T).令ax,t,u,Du)={aix,t,u,Du), 假设 aix,t,u,Du)与bx,t,u, Du)皆为 Caratheodory 函数, 并且假设它们满足Du的单调性, 关于u,|Du|等一定的增长阶条件下, 得到了解的比较定理,证明了解的存在性, 并得到了相关的Harnack不等式.

Abstract

In the paper, the Cauchy problem for the quasi-linear parabolic equation ut-div a(x, t,u, Du)=b(x,t, u, Du),(x,t), Suppose that ai(x,t,u,Du) and b(x,t,u,Du)are Caratheodory functions, and they satisfy some other restrictions such as the monotone property of Du the increasing order condition of u,|Du| etc., the comparison theorem of the equation is established, the existence of the solution is obtained, and the Harnack inequality is proved.

关键词

初始迹 / Harnack不等式 / 双非线性抛物方程

Key words

initial trace / Harnack inequality / doubly nonlinear parabolic equation

引用本文

导出引用
詹华税. 双非线性抛物方程初始迹与Harnack不等式. 数学学报, 2014, 57(3): 537-558 https://doi.org/10.12386/A2014sxxb0051
Hua Shui ZHAN. The Initial Trace and the Harnack Inequality of Doubly Nonlinear Parabolic Equations. Acta Mathematica Sinica, Chinese Series, 2014, 57(3): 537-558 https://doi.org/10.12386/A2014sxxb0051

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基金

福建省自然科学基金资助课题(2012J01011);厦门理工学院科研启动基金资助课题
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