| 非线性抛物型方程柯西问题整体光滑解存在唯一性 |
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| 引用本文： | 徐礼存,高剑敏.非线性抛物型方程柯西问题整体光滑解存在唯一性[J].同济大学学报(自然科学版),1986(1). |
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| 作者姓名： | 徐礼存 高剑敏 |
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| 作者单位： | 同济大学应用数学系
(徐礼存)，同济大学应用数学系(高剑敏) |
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| 摘 要： | 非线性抛物型方程整体解研究在理论,应用上都很重要,本文运用线性抛物型方程较丰满的能量估计和衰减估计,借助于Matsumura整体存在性框架,得到了在非线性项满足某种条件,空间维数不小于3且初值某种模适当小时,柯西问题整体解存在唯一性。
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| 关 键 词： | 能量估计 非线性抛物型方程 |
Existence and Uniqueness of Global and Smooth Solutions to Fully Nonlinear Parabolic Equations |
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| Xu Lichen Gao Jianmin.Existence and Uniqueness of Global and Smooth Solutions to Fully Nonlinear Parabolic Equations[J].Journal of Tongji University(Natural Science),1986(1). |
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| Authors: | Xu Lichen Gao Jianmin |
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| Institution: | Department of Applied Mathematics |
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| Abstract: | It is important in application and theory to study fully nonlinear parabolic equations. In this paper, we obtain unique global solutions for initial value problems of fully nonlinear parabolic equations under small initial data and fairly general conditions on nonlinear terms. The method of proof depends on efficient energy estimates and decay estimates of linear parabolic equations and follows Matsumura's framework of global existence. |
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| Keywords: | Energy estimation Nonlinear parabolic equations |
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