| 关于某类非线性发展方程的弱解 |
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| 引用本文： | 洪乃端. 关于某类非线性发展方程的弱解[J]. 厦门大学学报(自然科学版), 1987, 0(2) |
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| 作者姓名： | 洪乃端 |
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| 作者单位： | 夏门大学数学系 |
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| 摘 要： | 本文讨论如下非线性发展方程的初值问题 u_1 (f(u)) u-u_(xx)-u_(xxt)=0 (x,t)∈Ω×[0,T] u(x,0)=u_0(x) x∈Ω给出在某类Sobolev空间弱解的定义,利用Galerkin方法证明了该问题弱解的存在性,并用能量技巧证明了问题解的唯一性.
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The Weak Solution for Some Nonlinear Evolution Equations |
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| Hong Naiduan. The Weak Solution for Some Nonlinear Evolution Equations[J]. Journal of Xiamen University(Natural Science), 1987, 0(2) |
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| Authors: | Hong Naiduan |
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| Affiliation: | Department of Mathematics |
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| Abstract: | This paper considers the existence and the uniqueness of the weak solutions for the following nonlinear evolution equation problemIt is the generalized formula of the Benjamin-Bona-Mahouy equationBy using the Galerkin's method and a priori estimates, then by the limit procedure, the existence of the weak solution is obtained, and the uniqueness of the solution for the problem is proved. |
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| Keywords: | Weak solution Nonlinear evolution equation |
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