| Second Order Nonlinear Evolution Inclusions Ⅱ： Structure of the Solution Set |
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| 引用本文： | Nikolaos S. PAPAGEORGIOU Nikolaos YANNAKAKIS. Second Order Nonlinear Evolution Inclusions Ⅱ： Structure of the Solution Set[J]. 数学学报(英文版), 2006, 22(1): 195-206. DOI: 10.1007/s10114-004-0509-x |
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| 作者姓名： | Nikolaos S. PAPAGEORGIOU Nikolaos YANNAKAKIS |
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| 作者单位： | National Technical University, Department of Mathematics, Zografou Campus, Athens 157 80, Greece |
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| 摘 要： | We contimle the work initiated in [1] （Second order nonlinear evolution inclusions I： Existence and relaxation results. Acta Mathematics Science, English Series, 21（5）, 977-996 （2005）） and study the structural properties of the solution set of second order evolution inclusions which are defined in the analytic framework of the evolution triple. For the convex problem we show that the solution set is compact Rs, while for the nonconvex problem we show that it is path connected, Also we show that the solution set is closed only if the multivalued nonlinearity is convex valued. Finally we illustrate the results by considering a nonlinear hyperbolic problem with discontinuities.
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| 关 键 词： | 发展包含 紧密嵌入 双曲线方程 存在性 凸函数 |
| 收稿时间： | 2003-08-01 |
| 修稿时间： | 2003-08-012003-09-25 |
Second Order Nonlinear Evolution Inclusions II: Structure of the Solution Set |
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| Nikolaos S. Papageorgiou,Nikolaos Yannakakis. Second Order Nonlinear Evolution Inclusions II: Structure of the Solution Set[J]. Acta Mathematica Sinica(English Series), 2006, 22(1): 195-206. DOI: 10.1007/s10114-004-0509-x |
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| Authors: | Nikolaos S. Papageorgiou Nikolaos Yannakakis |
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| Affiliation: | (1) National Technical University, Department of Mathematics, Zografou Campus, Athens 157 80, Greece |
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| Abstract: | We continue the work initiated in [1] (Second order nonlinear evolution inclusions I: Existence and relaxation results. Acta Mathematics Science, English Series, 21(5), 977-966 (2005)) and study the structural properties of the solution set of second order evolution inclusions which are defined in the analytic framework of the evolution triple. For the convex problem we show that the solution set is compact R δ , while for the nonconvex problem we show that it is path connected. Also we show that the solution set is closed only if the multivalued nonlinearity is convex valued. Finally we illustrate the results by considering a nonlinear hyperbolic problem with discontinuities. |
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| Keywords: | Evolution triple Compact embedding Second order evolution Compact Rs Pathconnected Connected Continuum Hyperbolic problem |
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