2007 Fiscal Year Final Research Report Summary
MANY-FACETED ATTACK ON THE COMPLEX GINZBURG-LANDAU EQUATION
| Project/Area Number |
17540172
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Tokyo University of Science |
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Principal Investigator |
OKAZAWA Noboru Tokyo University of Science, MATHEMATICS, PROFESSOR (80120179)
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| Project Period (FY) |
2005 – 2007
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| Keywords | THE COMPLEX GINZBURG-LANDAU EQUATION / SMOOTHING EFFECT / LEBESGUE SPACE / SOBOLEV SPACE / EIGENVALUE OF LAPLACIAN / ESTIMATE OF EIGENFUNCTION / SCHROEDINGER OPERATORS / QUASI-M-ACCRETIVITY |
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| Research Abstract |
1) Initial-boundary value problems for the complex Ginzburg-Landau equation on a bounded domain is discussed when we take the initial values from the Lebesgue space L-p (p>2). As a corollary we can reformulate the result of Ginibre-Velo (1997) in which the initial values are taken from the Sobolev space H-1. In addition we can weaken the restriction on the exponents of the power of the nonlinear term if we take the initial values from H-m (m is a integer greater than or equal to 2). The stationary problems are also considered. (2) We have presented a new sufficient condition which guarantees the quasi-m-accretivity of Schroedinger operators with singular first-order coefficients. The result is regarded as an improvement of that by late Professor Tosio Kato. (3) We have obtained the estimates of the eigenfunctions e_n of the Laplace operator on a bounded domain. | (e_n) (x) | is bounded by the constant multiple of the eigenvalue to the power of N/4. This exponent with N=1 appears in the estimates of the eigenfunctions of the Schroedinger operator of the one-dimensional harmonic ocsilltor.
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Research Products
(10 results)
