一类无穷阶退化抛物方程解的存在性

李珂陈化

数学学报 ›› 2008, Vol. 51 ›› Issue (6) : 1089-109.

数学学报 ›› 2008, Vol. 51 ›› Issue (6) : 1089-109. DOI: 10.12386/A2008sxxb0126
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一类无穷阶退化抛物方程解的存在性

    李珂陈化
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Existence of Solutions for a Class of Infinitely Degenerate Parabolic Equations

    Ke LIHua CHEN
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摘要

X=(X1,,Xm)是一组无穷阶退化向量场, ΔX=j=1mXjXj, 其中XjXj的形式自伴算子. 运用不动点理论得到抛物方程ut=ΔXu+ulog|u|解的存在性.

Abstract

Let X=(X1,,Xm) be an infinitely degenerate system of vector fields, ΔX=j=1mXjXj, where Xj is the formal adjoint of Xj. By employing the fixed point theorem, we obtain the existence of solutions to the degenerate parabolic equation ut=ΔXu+ulog|u|.

关键词

退化抛物方程 / 对数Sobolev不等式 / H\"{o}rmander条件

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李珂陈化. 一类无穷阶退化抛物方程解的存在性. 数学学报, 2008, 51(6): 1089-109 https://doi.org/10.12386/A2008sxxb0126
Ke LIHua CHEN. Existence of Solutions for a Class of Infinitely Degenerate Parabolic Equations. Acta Mathematica Sinica, Chinese Series, 2008, 51(6): 1089-109 https://doi.org/10.12386/A2008sxxb0126

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