トップ›研究者を探す›非線形放物型方程式の自己相似性と解の特異性

非線形放物型方程式の自己相似性と解の特異性

KAKEN 科学研究費助成事業データベース で見る
研究課題番号 KAKENHI-PROJECT-20540210
研究種目 基盤研究(C)
研究分野 理工系
数物系科学
数学
大域解析学
研究機関 愛媛大学
神戸大学
代表研究者 内藤 雄基
研究分担者 石井 克幸
研究分担者 桑村 雅隆
連携研究者 鈴木 貴
連携研究者 仙葉 隆
連携研究者 石毛 和弘
研究期間 開始年月日 2008/4/1
研究期間 終了年度 2010
研究ステータス 完了 (2011/4/1)
配分額（合計） 4,290,000 (直接経費 :3,300,000、間接経費 :990,000)
配分額（履歴） 2011年度：1,040,000 (直接経費 :800,000、間接経費 :240,000)
2010年度：1,040,000 (直接経費 :800,000、間接経費 :240,000)
2009年度：1,040,000 (直接経費 :800,000、間接経費 :240,000)
2008年度：1,170,000 (直接経費 :900,000、間接経費 :270,000)
キーワード 非線形偏微分方程式
自己相似性
解の爆発
特異性
定常問題
非線形放物型偏微分方程式
自己相似解
Sobolev臨界指数
非線形楕円型偏微分方程式
変分法
走化性方程式系
p-Laplace方程式
爆発現象
非線形熱方程式

研究成果

[雑誌論文] Non-homogeneous semilinear elliptic equations involving critical Sobolev exponent

Yuki Naito, Tokushi Sato 2011

[雑誌論文] Non-homogeneous semilinear elliptic equations involving critical Sobolev exponent

Yuki Naito, Tokushi Sato 2011

[雑誌論文] Existence and non-existence of sign-changing solutions for a class of two-point boundary value problems involving one-dimensional p-Laplacian

Yuki Naito 2011

[雑誌論文] Existence and non-existence of sign-changing solutions for a class of two-point boundary value problems involving one-dimensional p-Laplacian

Yuki Naito 2011

[学会発表] Non-homogeneous semilinear elliptic equations involving critical Sobolev exponent

Yuki Naito 2011

[雑誌論文] Non-homogeneous semilinear elliptic equations involving critical Sobolev exponent

Yuki Naito, Tokushi Sato 2011

[雑誌論文] Existence and non-existence of sign-changing solutions for a class of two-point boundary value problems involving one-dimensional p-Laplacian

Yuki Naito 2011

[雑誌論文] Existence and non-existence of sign-changing solutions for a class of two-point boundary value problems involving one-dimensional p-Laplacian

Y.Naito 2010

[学会発表] Asymptotic behavior of solutions to the Cauchy problem for a semilinear heat equation

内藤雄基 2010

[学会発表] The role of self-similarity in the Cauchy problems for semilinear heat equations

Yuki Naito 2010

[学会発表] 臨界Sobolev指数をもつ非済次半線形楕円型偏微分方程式

佐藤得志、内藤雄基 2010

[学会発表] Asymptotic behavior of solutions to the Cauchy problem for a semilinear heat equation

Yuki Naito 2010

[学会発表] The role of self-similarity in the Cauchy problems for semilinear heat equations

内藤雄基 2010

[雑誌論文] Self-similar blow-up for a chemotaxis system in higher dimensional domains

Yuki Naito, Takasi Senba 2009

[学会発表] Non-homogeneous semilinear elliptic equations involving critical Sobolev exponent

内藤雄基 2009

[雑誌論文] Self-similar blow-up for a chemotaxis system in higher dimensional domains

Y.Naito, T.Senba 2009

[学会発表] A variational approach for self-similar solutions to nonlinear heat equations

Yuki Naito 2009

[雑誌論文] Non-homogeneous semilinear elliptic equations involving critical Sobolev exponent

Y. Naito, T. Sato 2009

[学会発表] Blowup rate for a parabolic-elliptic system in higher dimensional domains

Yuki Naito 2009

[学会発表] Self-similar blowup for a chemotaxis system

内藤雄基 2009

[学会発表] 高次元領域における走化性方程式系の解の自己相似爆発

仙葉隆、内藤雄基 2009

[雑誌論文] Non-homogeneous semilinear elliptic equations involving critical Sobolev exponent

Y.Naito, T.Sato 2009

[雑誌論文] Self-similar blow-up for a chemotaxis system in higher dimensional domains

Yuki Naito, Takasi Senba 2009

[雑誌論文] Non-homogeneous semilinear elliptic equations involving critical Sobolev exponent

Y. Naito, T. Sato 2009

[学会発表] Self-similar blowup for a chemotaxis system

Yuki Naito 2009

[学会発表] Critical phenomena in linear elliptic problem with Hardy potential

内藤雄基 2009

[学会発表] A variational approach for self-similar solutions to nonlinear heat equations

内藤雄基 2009

[学会発表] Blowup rate for a parabolic-elliptic system in higher dimensional domains

Yuki Naito 2009

[雑誌論文] Self-similar solutions for a semilinear heat equation with critical Sobolev exponent

Yuki Naito 2008

[学会発表] A variational approach for self-similar solutions to anonlinear heat equation with critical Sobolev exponent

Yuki Naito 2008

[雑誌論文] Self-Similarity in Chemotaxis Systems

Yuki Naito, Takashi Suzuki 2008

[雑誌論文] Self-similar solutions for a semilinear heat equation with critical Sobolev exponent

Yuki Naito 2008

[雑誌論文] Self-Similarity in Chemotaxis Systems

Yuki Naito, Takashi Suzuki 2008

[学会発表] Non-homogeneous semilinear elliptic equations involving critical Sobolev exponent

Yuki Naito 2008

[雑誌論文] Self-Similarity in Chemotaxis Systems

Yuki Naito, Takashi Suzuki 2008

[学会発表] Non-homogeneous semilinear elliptic equations involvingcritical Sobolev exponent

Yuki Naito 2008

[雑誌論文] Self-similar solutions for a semilinear heat equation with critical Sobolev exponent

Yuki Naito 2008

[雑誌論文] Sharp conditions for the existence of sign-changing solutions to equations involving the one-dimensional p-Laplacian

Yuki Naito, Satoshi Tanaka 2008

[学会発表] Self-similar blowup for a chemotaxis system in higher dimensional domains

Yuki Naito 2008

[雑誌論文] Sharp conditions for the existence of sign-changing solutions to equations involving the one-dimensional p-Laplacian

Yuki Naito, Satoshi Tanaka 2008

[学会発表] Threshold solutions for a seimilinear heat equation with Sobolev critical exponent

Yuki Naito 2008

[学会発表] Threshold solutions for a seimilinear heat equation with Sobolev critical exponent

Yuki Nai to 2008

[雑誌論文] Sharp Conditions for the ex istence of sign-changing solutions to equations involving the one-dimensionalp-Laplacian

Yuki Nai to, Satoshi Tanaka 2008

[学会発表] A variational approach for self-similar solutions to a nonlinear heat equat ion with critical Sobolev exponent

Yuki Nai to 2008

[学会発表] Self-similar blowup for a chemotaxis system in higher dimensional domains

Yuki Nai to 2008

[学会発表] Non-homogeneous semilinear elliptic equat ions involving critical Sobolev exponent

Yuki Naito 2008

[学会発表] Non-homogeneous semilinear elliptic equations involving critical Sobolev exponent

Yuki Naito 2008