1999 Fiscal Year Annual Research Report

ブラウン運動と非線型境界値問題

Research Project

Project/Area Number	10440050
Research Institution	University of Tsukuba
Principal Investigator	平良和昭筑波大学, 数学系, 教授 (90016163)
Co-Investigator(Kenkyū-buntansha)	梅津健一郎前橋工科大学, 工学部, 講師 (00295453) 木下保筑波大学, 数学系, 助手 (90301077) 南就将筑波大学, 数学系, 助教授 (10183964) 坂元国望広島大学, 理学部, 助教授 (40243547) 久保泉広島大学, 理学部, 教授 (70022621)
Keywords	ブラウン運動 / 境界値問題 / フェラー半群 / 人口動態論 / 化学反応論 / 調和積分論
Research Abstract	本年度の研究実績は、以下の4つの研究テーマに分類される: 1.まず、確率論における「拡散過程の境界値問題」に偏微分方程式的手法を適用し、退化する楕円型微分方程式の場合について、一般のヴェンツェル境界条件の下でのフェラー半群の存在定理を証明した。さらに、確率論におけるマルコフ過程構成の問題から派生した楕円型積分微分作用素の境界値問題に対する古典解の一意存在定理を証明した。 2.次に、数学的に未開拓な分野である数理生態学の「人口動態論」を非線型境界値問題と捉えて、詳しく考察した。これは、古典的なマルサス及びフェアフルストの人口動態論を数学的な立場から説明する試みである。 3.また、アレニウスの法則とニュートンの冷却の法則をみたす「化学反応物に対する燃焼問題」を考察した。特に、活性化エネルギーが十分小さい場合及び活性化エネルギーが十分大きい場合について、断熱状態の化学反応現象の時間的な安定性の問題を、解の分岐理論を援用して、数学的に考察した。 4.最後に、微分幾何学と関連して、古典的なホッジ・小平の調和積分論を相対的ドラームコホモロジー群の場合に拡張し、指定定理を解析的手法によって証明した。最も本質的な点は、指数公式が成り立つような作用素とカレントの関数空間を如何に定義するかである。

Research Products
(18 results)

All Other

All Publications (18 results)

[Publications] Kazuaki Taira: "Feller semigroups with boundary conditions"Rendiconti del Circolo Matematico di Palermo. 52・1. 157-173 (1998)
[Publications] Kazuaki Taira: "Boundary value problems of nonlinear elastostatics"Proceedings of the Conference Generalized Analytic Functions. 183-195 (1998)
[Publications] Kazuaki Taira: "Growing-up positive solutions of semilinear elliptic boundary value problems"Journal of Mathematical Analysis and Applications. 238・1. 196-215 (1999)
[Publications] Kazuaki Taira: "Feller semigroups and degenerate elliptic operators I"Conference del Seminario di Matematica dell'Universita di Bari. 274. 1-32 (1999)
[Publications] Kazuaki Taira: "Feller semigroups and degenerate elliptic operators II"Conference del Seminario di Matematica dell'Universita di Bari. 275. 1-33 (1999)
[Publications] Kazuaki Taira: "Brownian wotion,de Rham complex and index formulas"Trends in Probability and Related Analysis. 159-176 (1999)
[Publications] Kazuaki Taira: "Feller semigroups generated by degenerate elliptic operators"Semigroup Forum. 60・1. 1-14 (2000)
[Publications] Kazuaki Taira: "Stability in chemical reactor theory"Proceedings of the Conference on Evolution Equations and Their Applications in Physical and Life Sciences. (2000)
[Publications] Nariyuki Minami: "On the Poisson limit theorems of Sirai and Major"Communications in Mathematical Physics. (2000)
[Publications] Tamotu Kinoshita: "On third order hyperbolic equations"Journal d'Analyse Math'ematique. 77・1. 287-314 (1999)
[Publications] Kenichiro Umezu: "Positive solutions of a forced nonlinear elliptic boundary value problems"Journal of the Mathematical Society of Japan. 51・4. 801-815 (1999)
[Publications] Kenichiro Umezu: "Nonlinear elliptic boundary value problems suggested by fermentation"Nonlinear Differential Eguations and Applications. 7・1. (2000)
[Publications] Kenichiro Umezu: "Global positive solution branches of positone problems with nonlinear boundary conditions"Differential and Integral Eguations. 13・1. (2000)
[Publications] Izumi Kubo: "White noise analysis associated with seguences of numbers"Infinite Dimensional Analysis,Quantum Probability and Related topics. 2・3. 315-336 (1999)
[Publications] Kunimochi Sakamoto: "Asymptotic expansion of interface eguation for a reaction-diffusion system"Tohoku Mathematical Publications. 8・1. 149-158 (1998)
[Publications] Hiroyuki Takamura: "Remarks on the blow-up boundaries and rates for nonlinear wave eguations"Nonlinear Analysis. 33・2. 693-698 (1998)
[Publications] Tetsutaro Shibata: "Nonlinear multiparameter Sturm-Liouville problems"Asymptotic Analysis. 18・1. 173-192 (1998)
[Publications] Takayuki Kobayashi: "On global motion of a compressible viscous fluid with boundary slip condition"Applicationes Mathematicae. 26・2. 159-194 (1999)

1999 Fiscal Year Annual Research Report

ブラウン運動と非線型境界値問題

Principal Investigator

平良 和昭 筑波大学, 数学系, 教授 (90016163)

Research Products

[Publications] Kazuaki Taira: "Feller semigroups with boundary conditions"Rendiconti del Circolo Matematico di Palermo. 52・1. 157-173 (1998)

[Publications] Kazuaki Taira: "Boundary value problems of nonlinear elastostatics"Proceedings of the Conference Generalized Analytic Functions. 183-195 (1998)

[Publications] Kazuaki Taira: "Growing-up positive solutions of semilinear elliptic boundary value problems"Journal of Mathematical Analysis and Applications. 238・1. 196-215 (1999)

[Publications] Kazuaki Taira: "Feller semigroups and degenerate elliptic operators I"Conference del Seminario di Matematica dell'Universita di Bari. 274. 1-32 (1999)

[Publications] Kazuaki Taira: "Feller semigroups and degenerate elliptic operators II"Conference del Seminario di Matematica dell'Universita di Bari. 275. 1-33 (1999)

[Publications] Kazuaki Taira: "Brownian wotion,de Rham complex and index formulas"Trends in Probability and Related Analysis. 159-176 (1999)

[Publications] Kazuaki Taira: "Feller semigroups generated by degenerate elliptic operators"Semigroup Forum. 60・1. 1-14 (2000)

[Publications] Kazuaki Taira: "Stability in chemical reactor theory"Proceedings of the Conference on Evolution Equations and Their Applications in Physical and Life Sciences. (2000)

[Publications] Nariyuki Minami: "On the Poisson limit theorems of Sirai and Major"Communications in Mathematical Physics. (2000)

[Publications] Tamotu Kinoshita: "On third order hyperbolic equations"Journal d'Analyse Math'ematique. 77・1. 287-314 (1999)

[Publications] Kenichiro Umezu: "Positive solutions of a forced nonlinear elliptic boundary value problems"Journal of the Mathematical Society of Japan. 51・4. 801-815 (1999)

[Publications] Kenichiro Umezu: "Nonlinear elliptic boundary value problems suggested by fermentation"Nonlinear Differential Eguations and Applications. 7・1. (2000)

[Publications] Kenichiro Umezu: "Global positive solution branches of positone problems with nonlinear boundary conditions"Differential and Integral Eguations. 13・1. (2000)

[Publications] Izumi Kubo: "White noise analysis associated with seguences of numbers"Infinite Dimensional Analysis,Quantum Probability and Related topics. 2・3. 315-336 (1999)

[Publications] Kunimochi Sakamoto: "Asymptotic expansion of interface eguation for a reaction-diffusion system"Tohoku Mathematical Publications. 8・1. 149-158 (1998)

[Publications] Hiroyuki Takamura: "Remarks on the blow-up boundaries and rates for nonlinear wave eguations"Nonlinear Analysis. 33・2. 693-698 (1998)

[Publications] Tetsutaro Shibata: "Nonlinear multiparameter Sturm-Liouville problems"Asymptotic Analysis. 18・1. 173-192 (1998)

[Publications] Takayuki Kobayashi: "On global motion of a compressible viscous fluid with boundary slip condition"Applicationes Mathematicae. 26・2. 159-194 (1999)

平良和昭筑波大学, 数学系, 教授 (90016163)