| 一类微分算子生成的半群与发展方程初值问题的解 |
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| 引用本文： | 李存华. 一类微分算子生成的半群与发展方程初值问题的解[J]. 内蒙古大学学报(自然科学版), 1992, 23(1): 43-48 |
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| 作者姓名： | 李存华 |
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| 作者单位： | 淮海大学数学系 |
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| 摘 要： | 本文首先给出并讨论了一类广义微分算子A_(2k)=(-1)~(k-1)D~(2k);(A_(2k-1)=(-1)~(k-1)D~(2k-1))在定义域H~(2k)(H~(2k 1)))上生成的强连续半群.讨论了算子及其生成半群的自伴性,谱性,并将其应用于发展方程Cauchy问题,给出了一类线性偏微分方程的解.
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| 关 键 词： | 无穷小母元 发展方程 |
A Class of Semi-groups and the Solutions of Evolution Equations |
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| Li Cunhua Huai Hai University. A Class of Semi-groups and the Solutions of Evolution Equations[J]. Acta Scientiarum Naturalium Universitatis Neimongol, 1992, 23(1): 43-48 |
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| Authors: | Li Cunhua Huai Hai University |
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| Affiliation: | Li Cunhua Huai Hai University |
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| Abstract: | We discuss a class of strongly continuous semigroups and their infinitesimal generators-a class of sclfadjoint negative definite generalized differential operators.Applying the relation between the semi-groups and their generators to the theory of evolution equation,we obtain the solutions for a class of Cauchy problems of partial differential equations. |
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| Keywords: | infinitesimal generator evolution equation |
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