| 一类具有非线性边界条件的退化抛物型方程整体弱解的存在唯一性 |
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| 引用本文： | 朴东哲.一类具有非线性边界条件的退化抛物型方程整体弱解的存在唯一性[J].延边大学理工学报,2013,0(4):244-247. |
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| 作者姓名： | 朴东哲 |
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| 作者单位： | 延边大学理学院数学系,吉林延吉133002 |
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| 摘 要： | 讨论了一类具有非线性边界条件和非线性源项的退化抛物型方程的整体弱解的存在唯一性．首先给出了经典解的一致估计，然后利用弱解的比较原理以及分析方法证明了该问题整体弱解的存在唯一性．在宽松的条件下，本文推广了已知的有关结果．
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| 关 键 词： | 非线性边界条件 退化抛物型方程 整体弱解 存在唯一性 |
Existence and uniqueness of global weak solutions for a degenerate parabolic equation with a nonlinear boundary condition |
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| PIAO Dongzhe.Existence and uniqueness of global weak solutions for a degenerate parabolic equation with a nonlinear boundary condition[J].Journal of Yanbian University (Natural Science),2013,0(4):244-247. |
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| Authors: | PIAO Dongzhe |
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| Affiliation: | PIAO Dongzhe ( Department of Mathematics, College of Science, Yanbian University, Yanji 133002, China ) |
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| Abstract: | We study existence and uniqueness of global weak solutions for a degenerate parabolic equation with a nonlinear boundary condition and a nonlinear source term. We first give a uniform estimate for classical solutions. Then, we prove existence and uniqueness of global weak solutions to the problem by the comparison principle for weak solutions and the analysis method. Some result is generalized under more relaxed conditions. |
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| Keywords: | degenerate parabolic equation nonlinear boundary condition uniform estimate comparison principle |
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