| 任意维数的强阻尼非线性波动方程（Ⅰ）—初边值问题 |
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| 引用本文： | 刘亚成,刘大成.任意维数的强阻尼非线性波动方程（Ⅰ）—初边值问题[J].应用数学,1995,8(3):262-266. |
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| 作者姓名： | 刘亚成 刘大成 |
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| 作者单位： | 哈尔滨船舶工程学院，哈尔滨船舶工程学院，攀枝花钢铁研究院 哈尔滨 150001，哈尔滨 150001，617000 |
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| 摘 要： | 本文研究任意维数的强阻非线性波动方程ｕｔｔ－ａΔｕｔ－Δｕ＝ｆ（ｕ）具第一类齐边界条件的初值问题，设ｆ∈Ｃ＾１，ｆ＾１（ｕ）上方有界，且当ｎ≥４时存在常数Ａ，Ｂ和ｐ，使｜ｆ＾１（ｕ）｜≤Ａ｜ｕ｜＾ｐ＋Ｂ，其中０＜ｐ≤４／（ｎ－４）（ｎ＞４）：０＜ｐ＜∞（ｎ＝４），得到唯一整体强解，从而改进和推广了已知结果。
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| 关 键 词： | 强阻尼 非线性 波动方程 初边值问题 |
Strongly Damped Nonlinear Wave Equation in Arbitrary Dimensions( I )--Initial-Boundary Value Problem |
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| Liu Yacheng Wang Feng.Strongly Damped Nonlinear Wave Equation in Arbitrary Dimensions( I )--Initial-Boundary Value Problem[J].Mathematica Applicata,1995,8(3):262-266. |
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| Authors: | Liu Yacheng Wang Feng |
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| Abstract: | In this paper we study the initial-boundary value problem with first homogeneous boundary condition for the strongly damped nonlinear wave equation in arbitrary dimensions. Suppose that is upper bounded and when n>4, there exist
A,B and p such that then the unique global strong solution can be obtained, so the known results are improved and generalized. |
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| Keywords: | Strongly damp Nonlinear wave equation Arbitrary dimensions Initial-boundary value |
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