A blowup condition for solutions of the nonlinear integro-partial differential equation that describes population explosions

• Project/Area Number: 21540141
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Osaka Prefecture University
• Principal Investigator: TABATA Minoru 大阪府立大学, 工学研究科, 教授 (70207215)
• Co-Investigator(Kenkyū-buntansha): ESHIMA Nobuoki 大分大学, 医学部, 教授 (20203630) ; TAKAGI Ichiro 東海大学, 総合経営学部, 教授 (90226746)
• Project Period (FY): 2009 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000); Fiscal Year 2011: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2009: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
• Keywords: 人口爆発 / 人口移動 / マスター方程式 / 非線形偏微分積分方程式 / 数理モデル / 偏微分積分方程式 / 人口移動理論 / 非線形関数方程式 / 数理社会学 / 数値シミュレーション

Research Abstract

We succeed in proving the following proposition : there exists a positive constant such that if initial total population and the gradient of the initial population density are larger than the positive constant, then the mixed problem for the nonlinear integro-partial differential equation that describes population explosions has a blowup solution, which converges to Dirac delta function in the sense of distribution.

Research Products

• [Journal Article] A mathematical modeling approach to the formation of urban and rural areas : Convergence of global solutions of the mixed problem for the master equation in sociodynamics (2011)
  • Author(s): Minoru Tabata, Nobuoki Eshima, and Ichiro Takagi
  • Journal Title: Elsevier Science Volume: Vol.12, Issue 6 Pages: 3261-3293
• [Journal Article] Three predictive power measures for generalized linear models : Entropy coefficient of determination, entropy correlation coefficient and regression correlation coefficient (2011)
  • Author(s): Nobuoki Eshima and Minoru Tabata
  • Journal Title: Computational Statistics & Data Analysis Volume: Vol.55 Pages: 3049-3058
• [Journal Article] Three predictive power measures for generalized linear models : Entropy coefficient of determination, entropy correlation coefficient and regression correlation coefficient (2011)
  • Author(s): Nobuoki Eshima, Minoru Tabata
  • Journal Title: Computational Statistics & Data Analysis Volume: 55 Issue: 11 Pages: 3049-3058
  • DOI: 10.1016/j.csda.2011.05.018
  • Peer Reviewed
• [Journal Article] A mathematical modeling approach to the formation of urban and rural areas : Convergence of global solutions of the mixed problem for the master equation in sociodynamics (2011)
  • Author(s): Minoru Tabata, Nobuoki Eshima, Ichiro Takagi
  • Journal Title: Nonlinear Analysis Series B : Real World Applications Volume: 12 Issue: 6 Pages: 3261-3293
  • DOI: 10.1016/j.nonrwa.2011.05.025
  • Peer Reviewed
• [Journal Article] Nonlinear Analysis Series B : Real World Applications, Elsevier Science, Amsterdam (2010)
  • Author(s): Minoru Tabata, Nobuoki Eshima, and IchiroI Takagi
  • Journal Title: Elsevier Science Volume: Vol.11, Issue 5 Pages: 4027-4042
• [Journal Article] Entropy coefficient of determination for generalized linear models (2010)
  • Author(s): Nobuoki Eshima and Minoru Tabata
  • Journal Title: Computational Statistics & Data Analysis, Elsevier Science Volume: Volume 54, Issue 5 Pages: 1381-1389
• [Journal Article] Sexand age-related differences in morbidity rates of 2009 pandemic influenza A H1N1 virus of swine origin in Japan (2010)
  • Author(s): Nobuoki Eshima, Osamu Tokumaru, Shohei Hara, Kira Bacal, Seigo Korematsu, Minoru Tabata, Shigeru Karukaya, Yoshinori Yasui, Nobuhiko Okabe, Toyojiro Matsuishi
  • Journal Title: PLoS ONE Volume: 6(4) Issue: 4 Pages: 1261-1293
  • DOI: 10.1371/journal.pone.0019409
  • URL: http://dx.plos.org/10.1371/journal.pone.0019409
  • Peer Reviewed
• [Journal Article] Entropy coefficient of determination for generalized linear models (2010)
  • Author(s): Nobuoki Eshima, Minoru Tabata
  • Journal Title: Computational Statistics & Data Analysis, Elsevier Science Volume: 54 Pages: 1381-1389
  • Peer Reviewed
• [Journal Article] A mathematical-model approach to human population explosions caused by migration (2010)
  • Author(s): Minoru Tabata, Nobuoki Eshima, Ichirol Takagi
  • Journal Title: Nonlinear Analysis Series B : Real World Applications, Elsevier Science Volume: 11 Pages: 4027-4042
  • Peer Reviewed
• [Journal Article] Age and gender specific prevalence of HTLV-1 : a hidden paradox (2009)
  • Author(s): Nobuoki Eshima, Osuke Iwata, Sachiko Iwata, Minoru Tabata, Yasunori Higuchi, Toyojiro Matsuishi, and Shigeru Karukaya
  • Journal Title: Journal of Clinical Virology, Elsevier Science Volume: Volume 45, Issue 2 Pages: 135-138
• [Journal Article] The Kramers-Moyal expansion of the master equation that describes human migration in a bounded domain (2009)
  • Author(s): Minoru Tabata and Nobuoki Eshima
  • Journal Title: Elsevier Science Volume: Vol.10 Pages: 639-664
• [Journal Article] The Kramers-Moyal expansion of the master equation that describes human migration in bounded domain (2009)
  • Author(s): M.Tabata, N.Eshima
  • Journal Title: Nonlinear Analysis Series B : Real World Applications, Elsevier Science 10 Pages: 639-664
  • Peer Reviewed
• [Journal Article] (2009)
  • Author(s): M.Tabata, T.Moriyama, S.Motoyama, N.Eshima
  • Journal Title: A mathematical-model approach to chlamydial infection in Japan. In : Progress in Nonlinear Analysis Research ISBN : 978-1-60456-359-7(Nova Science Publishers, Inc) Pages: 25-33
• [Book] Partial Differential Equations : Theory, Analysis and Applications (2011)
  • Author(s): Minoru Tabata and Nobuoki Eshima
  • Publisher: 2010 Nova Science Publishers
• [Book] A stochastic agent-based approach to the Fokker-Planck equation in human population dynamics, In : Partial Differential Equations : Theory, Analysis and Applications, Editor : Christopher L, ISBN : 978-1-61122-858-8 (2011)
  • Author(s): Minoru Tabata, Nobuoki Eshima
  • Total Pages: 15
  • Publisher: Nova Science Publishers, Inc
• [Book] Progress in Nonlinear Analysis Research (2009)
  • Author(s): M. Tabata, T. Moriyama, S. Motoyama, and N. Eshima
  • Publisher: 2009 Nova Science Publishers
• [Remarks]