2001 Fiscal Year Annual Research Report

偏微分方程式、変分問題、逆問題の解の総合的研究

Research Project

Project/Area Number	13640183
Research Institution	Tokyo Metropolitan University
Principal Investigator	倉田和浩東京都立大学, 理学研究科, 助教授 (10186489)
Co-Investigator(Kenkyū-buntansha)	田中和永早稲田大学, 理工学部, 教授 (20188288) 肥田野久二雄東京都立大学, 理学研究科, 助手 (00285090) 望月清東京都立大学, 理学研究科, 教授 (80026773) 村田実東京工業大学, 理工学研究科, 教授 (50087079) 神保秀一北海道大学, 理学研究科, 教授 (80201565)
Keywords	Cahn-Hilliardエネルギー / Schrodinger作用素 / 最適化問題 / ギンツブルグ-ランダウ方程式 / Allen-Cahn方程式 / 放物型方程式の解の一意性 / 逆スペクトル問題 / 非線型波動方程式
Research Abstract	1.倉田は次の研究を行った。 (1)2次元の曲がった帯状領域上でのCahn-Hilliardエネルギーに関係する1次元の空間非一様な重みをもつ変分問題の最小解の単調性の崩れをrearrangementの手法とΓ-収束の理論を用いて調べた。 (2)Schrodinger作用素のDirichlet第一固有値に関する最適化問題の研究を続け、今回オブスタクルの形をあらかじめ球と指定した場合の最適位置の決定を論じた。 (3)遠方で減衰するbackground metricにおけるChern-Simons-Higgs理論に現れる非線型楕円型方程式のnon-topologicalな解の存在を示した。 2.分担者の神保は、ギンツブルグ-ランダウ方程式の非定常問題の解の特異摂動極限におけるゼロ点運動の特徴つけや慣性多様体の構成を行い、田中は-Δu+u=g(x,u)+f(x)の正値解の存在を示したり、Allen-Cahn方程式を代表するbistableな方程式で1点に集中する遷移層をもつ解の変分的構成に成功した。村田は、リーマン多様体上の放物型方程式に対する初期値問題の非負値解の一意性が成立するための最適十分条件を与えた。 3.望月は、Sturm-Liouville作用素のひとつのスペクトルと内部の1点での固有関数の情報からの逆スペクトル問題の一意性を示した。肥田野は、非線型波動方程式の小さい解の時間無限大における挙動を散乱問題および自己相似性の観点から研究した。

Research Products

(16 results)

All Other

All Publications (16 results)

[Publications] Kazuhiro Kurata: "Existence of non-topological solutions for a nonlinear elliptic equation arising from Chern-Simons-Higgs theory in a general background metric"Duff. Integral Equations. 14. 925-935 (2001)
[Publications] Kazuhiro Kurata (with Masataka Shibata): "On a one-dimensional Variational Problem related to Cahn-Hilliard Energy on a Strip-Like Domain"Nonlinear Analysis. 47. 1059-1068 (2001)
[Publications] B.M.Harrell II(with P.Kroger, K.Kurata): "On the placement of an obstacle or a well so as to optimize the fumdamental eigenvalue"SIAM J Math. Ana.. 33. 240-259 (2001)
[Publications] Kazunaga Tanaka(with K.Nakashima): "Clustering layers and boundary layers in spatially inhomogeneous phase transition problems"to appear in Ann. Inst. H. Poincar e Anal. Non Lineaire. (2002)
[Publications] S.Adachi(with K.Tanaka): "Existence of positive solutions for a class of nonhomogeneous elliptic equations in R^N"Nonlinear Analysis : T.M.A.. 48. 685-705 (2002)
[Publications] S.Jimbo(with Y.Morita): "Notes on the limit equation of vortex motion for the Ginzburg-Landau equation with Neumann condition"Japan J. Indst. Appl. Math.. 18. 483-502 (2001)
[Publications] S.Jimbo(with Y.Morita): "Vortex dynamics for the Ginzburg-Landau equation with Neumann condition"to appear in Mathods and applications to Analysis. 8-2. (2002)
[Publications] S.Jimbo(with Y.Morita): "Ginzburg-Landau functional with magnetic effect in a thin domain"to appear in Calculus of Variations. (2002)
[Publications] 神保秀一: "ギンツブルグ・ランダウ方程式とボルテクス"応用数理. 11. 60-70 (2001)
[Publications] Minoru Murata(with Kazuhiro Ishige): "Uniqueness of nonnegative solutions of the Cauchy problem for parabolic equations on manifolds or domains"Ann. Scuola Norm. Sup. Pisa. 30. 171-223 (2001)
[Publications] Minoru Murata: "Martin boundaries of elliptic skew products, semismall perturbations, and fundamental solutions of parabolic equations"to appear in J. Func. Anal.. (2002)
[Publications] Mochizuki(with I.A.Shishmarev): "Large time asymptotics of small solutions to generalized Kolmogorov-Petrovskii-Piskunov equation"Funkcialai Ekvasioj. 44. 99-117 (2001)
[Publications] K.Mochizuki(with I.Trooshin): "Inverse problem for interior spectral data of Sturm-Liouville operator"J. Inv. Ill-Posed Prob.. 9. 425-433 (2001)
[Publications] K.Mochizuki(with H.Nakazawa): "Energy decay of solutions to the wave equation with linear dissipation localized near infinity"Publ. Res. Inst. Math. Sci.. 37. 441-458 (2001)
[Publications] Kunio Hidano: "Scattering and self-similar solution for the nonlinear wave equation"Diff. Int. Eqns.. 15. 405-462 (2002)
[Publications] Kunio Hidano: "Scattering problem for the nonlinear wave equation in the finite energy and conformal charge space"J. Funct. Anal.. 187. 274-307 (2001)

2001 Fiscal Year Annual Research Report

偏微分方程式、変分問題、逆問題の解の総合的研究

Principal Investigator

倉田 和浩 東京都立大学, 理学研究科, 助教授 (10186489)

Research Products

[Publications] Kazuhiro Kurata: "Existence of non-topological solutions for a nonlinear elliptic equation arising from Chern-Simons-Higgs theory in a general background metric"Duff. Integral Equations. 14. 925-935 (2001)

[Publications] Kazuhiro Kurata (with Masataka Shibata): "On a one-dimensional Variational Problem related to Cahn-Hilliard Energy on a Strip-Like Domain"Nonlinear Analysis. 47. 1059-1068 (2001)

[Publications] B.M.Harrell II(with P.Kroger, K.Kurata): "On the placement of an obstacle or a well so as to optimize the fumdamental eigenvalue"SIAM J Math. Ana.. 33. 240-259 (2001)

[Publications] Kazunaga Tanaka(with K.Nakashima): "Clustering layers and boundary layers in spatially inhomogeneous phase transition problems"to appear in Ann. Inst. H. Poincar e Anal. Non Lineaire. (2002)

[Publications] S.Adachi(with K.Tanaka): "Existence of positive solutions for a class of nonhomogeneous elliptic equations in R^N"Nonlinear Analysis : T.M.A.. 48. 685-705 (2002)

[Publications] S.Jimbo(with Y.Morita): "Notes on the limit equation of vortex motion for the Ginzburg-Landau equation with Neumann condition"Japan J. Indst. Appl. Math.. 18. 483-502 (2001)

[Publications] S.Jimbo(with Y.Morita): "Vortex dynamics for the Ginzburg-Landau equation with Neumann condition"to appear in Mathods and applications to Analysis. 8-2. (2002)

[Publications] S.Jimbo(with Y.Morita): "Ginzburg-Landau functional with magnetic effect in a thin domain"to appear in Calculus of Variations. (2002)

[Publications] 神保秀一: "ギンツブルグ・ランダウ方程式とボルテクス"応用数理. 11. 60-70 (2001)

[Publications] Minoru Murata(with Kazuhiro Ishige): "Uniqueness of nonnegative solutions of the Cauchy problem for parabolic equations on manifolds or domains"Ann. Scuola Norm. Sup. Pisa. 30. 171-223 (2001)

[Publications] Minoru Murata: "Martin boundaries of elliptic skew products, semismall perturbations, and fundamental solutions of parabolic equations"to appear in J. Func. Anal.. (2002)

[Publications] Mochizuki(with I.A.Shishmarev): "Large time asymptotics of small solutions to generalized Kolmogorov-Petrovskii-Piskunov equation"Funkcialai Ekvasioj. 44. 99-117 (2001)

[Publications] K.Mochizuki(with I.Trooshin): "Inverse problem for interior spectral data of Sturm-Liouville operator"J. Inv. Ill-Posed Prob.. 9. 425-433 (2001)

[Publications] K.Mochizuki(with H.Nakazawa): "Energy decay of solutions to the wave equation with linear dissipation localized near infinity"Publ. Res. Inst. Math. Sci.. 37. 441-458 (2001)

[Publications] Kunio Hidano: "Scattering and self-similar solution for the nonlinear wave equation"Diff. Int. Eqns.. 15. 405-462 (2002)

[Publications] Kunio Hidano: "Scattering problem for the nonlinear wave equation in the finite energy and conformal charge space"J. Funct. Anal.. 187. 274-307 (2001)

倉田和浩東京都立大学, 理学研究科, 助教授 (10186489)