| 一类非线性积分偏微分方程的初值问题 |
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| 引用本文： | 郭艾.一类非线性积分偏微分方程的初值问题[J].应用数学和力学,1999,20(6):640-646. |
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| 作者姓名： | 郭艾 |
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| 作者单位： | 甘肃工业大学数学教研室, 兰州 730050 |
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| 摘 要： | 讨论初值问题 整体经典解的存在性。该问题来源于粘弹性力学。在关于已知函数的一些正则性假设和p'(s)≥c1>0,|q'(s)|≤const,λ(0)<0,λ'(0)<λ2(0)的条件下,通过能量估计,证明了该问题整体经典解的存在性。
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| 关 键 词： | 初值问题 积分偏微分方程 经典解 |
| 收稿时间： | 1997-08-11 |
Initial Value Problems for a Class of Nonlinear Integro_Partial Differential Equations |
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| Guo Ai.Initial Value Problems for a Class of Nonlinear Integro_Partial Differential Equations[J].Applied Mathematics and Mechanics,1999,20(6):640-646. |
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| Authors: | Guo Ai |
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| Institution: | Gansu University of Technology, Lanzhou 730050, P R China |
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| Abstract: | In this paper,the problem of global existence of solutions to the followin g initial value problem is studied: which comes from viscoelastic mechanics.By making u se of integral estimates method,it is proved that this problem has a global solution if,in addition to certain regularity assumptions on the given fun ctions,the following conditions are satisfied: p'(s)≥c1>0,|q'(s)|≤const,λ(0)<0,λ'(0)<λ2(0). |
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| Keywords: | initial value problem integro_partial differential equation classical solution |
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