2013 Fiscal Year Final Research Report
Studies on well-posedness for parabolic equations with nonlinear constraints
| Project/Area Number |
23540206
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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 | Hiroshima University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
KOBAYASHI Yoshikazu 中央大学, 理工学部, 教授 (80092691)
WATANABE Hiroshi サレジオ工業高等専門学校, 助教 (30609912)
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| Co-Investigator(Renkei-kenkyūsha) |
TANAKA Naoki 静岡大学, 大学院・理学研究科, 教授 (00207119)
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| Project Period (FY) |
2011 – 2013
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| Keywords | 適切性 / 放物型方程式 / リプシッツ作用素半群 |
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| Research Abstract |
We studied well-posedness for parabolic equations and generation theorems of semigroups of Lipschitz operators. A nonlinear perturbation theory for analytic semigroups was extended to the case of analytic semigroups of growth order alpha. The obtained results were applied to showing the well-posedness of 2-D drift-diffusion equations with no-flux boundary conditions. Existence and uniqueness results for weak solutions to strongly degenerate parabolic equations and a phase filed model of grain boundary motion were also derived. Futhermore, we provided an approximation theorem for semigroups of Lipschitz operators and its application to 2-D Navier-Stokes equations as well as a characterization theorem for Lipschitz evolution operators in Banach spaces.
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