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総説・著書

 

M.Shimojo, 「非線形放物型方程式における交点数理論入門」, 芝浦工業大学応用数学勉強会レクチャーノート, pp. 96, (2016)

“Introduction to blow-up problems for nonlinear heat equations” (Lectured by Marek Fila), Seminary Note of Mathematical Science of The University of Tokyo (Japanese).

俣野博(監修), 下條昌彦(記), 「非線形熱方程式の爆発問題入門」- Marek Fila氏講義録-, 東京大学数理科学研究科(レクチャーノート10)(pp 248)(学術著書) 東京大学数理科学レクチャーノート,全248ページ (2011)

Blow-up at space infinity and criteria for total blow-up in nonlinear heat Equations, PhD Thesis, University of Tokyo, pp. 1-295 (2008)

 

原著論文(査読あり)

A-L Poh and M. Shimojo, Blow-up of radially symmetric solutions for a semilinear heat equation on Hyperbolic space, Revista Matemtica Complutense, Doi 10.1007/s13163-019- 00302-5, pp. 1–26 (2019)

M. Shimojo, P. Takáč, E. Yanagida, "Asymptotic Behavior of Solutions to the Logarithmic Diffusion Equation with a Linear Source",  Mathematische Annalen, vol. 372 pp. 429-449 (2018)

A. Ducrot, J. S. Guo, M.Shimojo, "Behaviors of solutions for a singular prey-predator model and its shadow system", Journal of Dynamics and Differential Equations, vol. 30 pp. 1063-1079 (2018)

M. Shimojo, Amy Poh Ai Ling, "Asymptotic behaviors of solutions to a reaction–diffusion equation with isochronous nonlinearity", Journal of Mathematical Analysis and Applications, vol. 462, Issue 2, pp. 1099-1108 (2018)

J. S. Guo, M. Shimojo "Spatio-temporal oscillation for a singular predator-prey model", Journal of Mathematical Analysis and Applications, vol. 459, Issue 1, pp.1-9 (2018)

M. Shimojo, P. Takac, E. Yanagida “Asymptotic behavior of solutions to the logarithmic diffusion equation with a linear source”, Mathematische Annalen (2017)

A. Ducrot, J-S Guo, and M. Shimojo, “Behaviors of solutions for a singular Prey-Predator model and its shadow system”, Journal of Dynamics and Differential Equations, pp.17 (2017)

J.S. Guo, M.Hiroshi, M.Shimojo, C.H. Wu, “On a free boundary problem for the curvature flow with driving force”, Archive for Rational Mechanics and Analysis, vol.219, Issue 3, pp.1207-1272 (2016)

M. Shimojo, K. Takashi “Exponential stability of a traveling wave for an area preserving curvature motion with two endpoints moving freely on a line”, Asymptotic Analysis, vol. 96, no. 2, pp. 109-134 (2016)

J.S. Guo, H. Ninomiya, M. Shimojo and E. Yanagida, "Convergence and blow-up of solutions for a complex-valued heat equation with a quadratic nonlinearity", Trans. Amer. Math. Soc. 365, 2447-2467  (2013)

J.S. Guo, C.S. Lin, M. Shimojo, “Blow-up for a reaction-diffusion equation with variable coefficient”, M, Appl. Math. Lett. 26(1): pp.150-153 (2013)

M. Shimojo, N. Umeda, “Blow-up at space infinity for solutions of cooperative reaction-diffusion systems”, Funkcialaj Ekvacioj, 54 315–334 (2011). 


J.S. Guo and M. Shimojo, Blowing up at the zero point of potential for an initial boundary value problem, Communication on Pure and Applied Analysis 10-1, Am. Inst. Math. Sci. (AIMS), pp.161-177 (2011)

 

Y.J.L. Guo,M. Shimojo, Blow-up for parabolic equations and system with nonnegative potential, Taiwanese Journal of Mathematics, 15-3, Math. Soc. Repub. China (Taiwan), pp.995-1005 (2011)

 

J.S. Guo , C.S. Lin and M. Shimojo, Blow-up behavior for a parabolic equation with spatially dependent coefficient, Dynamic Systems and Applications, 19-3, Dynamic Atlanta GA 30362-0654, pp.415-434 (2010)

 

M. Shimojo, The global profile of blow-up at space infinity for semilinear heat equations, Journal of Mathematics of Kyoto University 48-2, Kyoto University, pp.339-361 (2008)

原著論文(査読なし)

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