| 引用本文: | 孔荣,张蕊.半线性热传导方程Cauchy问题全局经典解的存在性与唯一性.[J].国防科技大学学报,1992,14(3):80-88.[点击复制] |
| Kong Rong,Zhang Rui.The Existence and Uniqueness of the Global Classic Solution to the Cauchy Problem of Semilinear Heat Transfer Equations[J].Journal of National University of Defense Technology,1992,14(3):80-88[点击复制] |
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| 半线性热传导方程Cauchy问题全局经典解的存在性与唯一性 |
| 孔荣, 张蕊 |
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(系统工程与应用数学系)
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| 摘要: |
| 本文证明了热传导方程Cauchy 问题
ut=uxx+ua x∈R,t>0
u|t=0=φ(x)
当实数α>3 时，只要初值φ(x)在某些Sobolev 空间中的范数充分小，就有唯一的全局经典解，且当t→+∞时，这个解具有一定的衰减性。本文所用的方法使得 Cauchy问题中的a的值同解与初值所在的空间紧密联系，a的值越大，解的性质越好。 |
| 关键词: 非线性偏微分方程，热传导方程，方程解，Cauchy 问题，全局解，经典解。 |
| DOI： |
| 投稿日期：1991-06-21 |
| 基金项目: |
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| The Existence and Uniqueness of the Global Classic Solution to the Cauchy Problem of Semilinear Heat Transfer Equations |
| Kong Rong, Zhang Rui |
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(Department of System Engineering and Applied Mathematics)
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| Abstract: |
| We investigated the existence and uniqueness of the cauchy problem of semilinear heat transfer equation. We proved that for α>3，if the initial value φ(x) is sufficiently small in some Sobolev spaces，there exists a unique global classic solution for the Cauchy problem. And the solution decays as t→+∞. The method used in this paper makes the value of α be closely combined with the spaces in which the sloution and initial value function are defined. The larger the value of α is，the better the properties of the solution are. |
| Keywords: non-linear partial differential equations,heat transfer equation,solution of equation cauchy prolblem,global solution,classic solution,existence,uniqueness,sobolev space |
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