2016 Fiscal Year Final Research Report
Well-posedness for partial differential equations with time-dependent constraints
| Project/Area Number |
26400138
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Shizuoka University (2015-2016)
Hiroshima University (2014) |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
TANAKA Naoki 静岡大学, 理学部, 教授 (00207119)
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Keywords | 準線形方程式 / 適切性 / リプシッツ発展作用素 / 変異方程式 |
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| Outline of Final Research Achievements |
We consider Cauchy problems for abstract evolution equations in Banach spaces where nonlinear operators are weakly continuous in some sense, and provide a necessary and sufficient condition for existence of weakly continuously differentiable solutions. We also discuss abstract quasilinear problems where the domain of quasilinear operators are neither dense nor constant, and prove a unique existence of continuously differentiable solutions. Under a generalised dissipativity condition, time local well-posedness for Cauchy problems to mutational equations are established. An existence and uniqueness result for entropy solutions to 1-D strongly degenerate parabolic equations is given. Finally phase field models related to grain boundary motions are considered. Existence of weak solutions which reproduce the energy-dissipation is shown and asymptotic behaviours of weak solutions are investigated.
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| Free Research Field |
実解析学
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