Existence and nonexistence of time-global solutions to damped wave equation on half-line
文献类型：期刊论文
| 作者 | Nishihara, K; Zhao, HJ |
| 刊名 | NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
 |
| 出版日期 | 2005-06-01 |
| 卷号 | 61期号:6页码:931-960 |
| 关键词 | semilinear damped wave equation global existence blow-up critical exponent |
| 英文摘要 | On the half-line R+ = (0, infinity) the initial-boundary value problems with null-Dirichlet boundary for both the semilinear heat equation and damped wave equation are considered. The critical exponent p(c) (N, k) of semilinear term for the existence and nonexistence about the semilinear heat equation on the halved space D-N,D-k = R-+(k) = RN-k is given by p(c)(N, k) = 1 + 2/(N + k) (J. Appl. Math. Phys. 39 (1988) 135-149; Arch. Rational Mech. Anal. 109 (1990) 63-71). Since the damped wave equation is expected to be close to the heat equation (J. Differential Equations 191 (2003) 445-469; Math. Z. 244 (2003) 631-649), the critical exponent for the semilinear damped wave equation is expected to be same as that of the semilinear heat equation. However, there is no blow-up result on the halved space for the damped wave equation. In this paper, the exponent pc(l, 1) = 2 is shown to be critical for the existence and nonexistence of time-global solution to both the semilinear heat equation and damped wave equation on the half-line R+, together with the derivation of the blow-up time. For the proof the explicit formulas of solutions are used in a similar fashion to those in Li and Zhou (Discrete Continuous Dynamic Systems 1 (1995) 503-520). (c) 2005 Elsevier Ltd. All rights reserved. |
| WOS标题词 | Science & Technology ; Physical Sciences |
| 类目[WOS] | Mathematics, Applied ; Mathematics |
| 研究领域[WOS] | Mathematics |
| 关键词[WOS] | PARABOLIC DIFFERENTIAL-EQUATIONS ; REACTION-DIFFUSION EQUATIONS ; CRITICAL EXPONENT ; BLOW-UP ; ASYMPTOTIC-BEHAVIOR ; R-N ; THEOREMS ; SPACE ; CONES |
| 收录类别 | SCI |
| 语种 | 英语 |
| WOS记录号 | WOS:000228630700004 |
| 公开日期 | 2015-07-28 |
| 源URL | [http://ir.wipm.ac.cn/handle/112942/4536]  |
| 专题 | 武汉物理与数学研究所_2011年以前论文发表（包括2011年） |
| 作者单位 | 1.Waseda Univ, Sch Polit Sci & Econ, Tokyo 1698050, Japan 2.Chinese Acad Sci, Wuhan Inst Phys & Math, Wuhan 430071, Peoples R China |
| 推荐引用方式 GB/T 7714 | Nishihara, K,Zhao, HJ. Existence and nonexistence of time-global solutions to damped wave equation on half-line[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS,2005,61(6):931-960. |
| APA | Nishihara, K,&Zhao, HJ.(2005).Existence and nonexistence of time-global solutions to damped wave equation on half-line.NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS,61(6),931-960. |
| MLA | Nishihara, K,et al."Existence and nonexistence of time-global solutions to damped wave equation on half-line".NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 61.6(2005):931-960. |
入库方式： OAI收割
来源：武汉物理与数学研究所
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