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| 任意维数半线性拟抛物方程的整体W2,p(2＜p＜∞)解 | |
| 引用本文： | 刘亚成,杜娟. 任意维数半线性拟抛物方程的整体W2,p(2＜p＜∞)解[J]. 黑龙江大学自然科学学报, 2004, 21(1): 6-10 |
| 作者姓名： | 刘亚成 杜娟 |
| 作者单位： | 1. 哈尔滨工程大学,理学院,黑龙江,哈尔滨,150001 2. 哈尔滨师范大学,理学院,黑龙江,哈尔滨,150080 |
| 基金项目： | Supported by National Natural Science Foundation of China(10271034) |
| 摘 要： | 研究有界域上的任意维数的半线性拟抛物方程的初边值问题ut-△ut=f(u)x∈Ω, t＞0 (1.1)u(x, 0)= u0(x) x∈Ω (1.2)u| Ω=0 t≥0 (1.3)利用逐次磨光法,证明了,若f∈C1,f(u)上方有界,且满足(H)|f′u)|≤A1|u|γ1+B1, 0≤γ1＜∞ ifn=4; 0≤γ1＜4/n-4 if n＞4u0(x)∈W2,p(Ω)∩W1,p0(Ω)(2＜p＜∞),则对任一T(x),问题(1.1)-(1.3)存在唯一整体解u(x,t)∈W2,∞(0,T;W2,p(Ω)∩W1,p0(Ω)).从实质上改进和推广了文献[1-3]的结果. |
| 关 键 词： | 半线性拟抛物方程 初边值问题 整体W2,p(2＜p＜∞)解 存在性 |
Global W2,p (2＜p＜∞) solutions of semilinear pseudoparabolic equations in arbitrary dimensions |
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| Abstract. Global W2,p (2＜p＜∞) solutions of semilinear pseudoparabolic equations in arbitrary dimensions[J]. Journal of Natural Science of Heilongjiang University, 2004, 21(1): 6-10 | |
| Authors: | Abstract |
| Abstract: | The initial boundary value problem on bounded domain for semilinear pseudoparabolicequations in arbitrary dimensions is studiedBy using successive smoothing method, it is proved that if is bounded above and satisfies then for any T(x) problem (1.1)~(1.3) admits a unique global solution The results of [1-3] are generalized and improved essentially. |
| Keywords: | semilinear pseudoparabolic equations initial boundary value problem global W~(2 p) solutions existence |
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