| 一类双曲型方程的Hamilton算子半群方法 |
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| 引用本文： | 徐娟娟,刘杰.一类双曲型方程的Hamilton算子半群方法[J].数学的实践与认识,2017(1):265-270. |
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| 作者姓名： | 徐娟娟 刘杰 |
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| 作者单位： | 内蒙古大学满洲里学院,内蒙古满洲里,021400 |
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| 基金项目： | 内蒙古自治区高等学校科学研究项目(NJZY16558) |
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| 摘 要： | 将一类双曲型方程混合问题转换成一阶抽象Cauchy问题,证明所得Hamilton算子矩阵H在相应空间中生成压缩半群,并借助Fourier变换,采用一致连续半群做逼近的方法,得到H所生成的压缩半群,进而给出了问题的古典解.
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| 关 键 词： | 双曲型方程 算子半群方法 压缩半群 古典解 |
Hamiltonian Operator Semigroup Method for A Class of Hyperbolic Equation |
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| XU Juan-juan,LIU Jie.Hamiltonian Operator Semigroup Method for A Class of Hyperbolic Equation[J].Mathematics in Practice and Theory,2017(1):265-270. |
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| Authors: | XU Juan-juan LIU Jie |
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| Abstract: | First,the mixed problem for a class of hyperbolic equation is transformed into a first-order abstract Cauchy problem.Then,it is proved that the Hamiltonian operator matrix generates a contraction semigroup in the corresponding space.Finally,by means of Fourier transform and uniformly continuous semigroup approximation,the expression of the contraction semigroup is obtained,and then the classical solution to the equation is given. |
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| Keywords: | hyperbolic equation operator semigroup method contraction semigroup classical solution |
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