Paper

  1. N. Ioku, K. Ishige and T. Kawakami, Existence of solutions to a fractional semilinear heat equation in uniformly local weak Zygmund type spaces, to appear in Anal. PDE
  1. T. Kawakami, Y. Sire and J.-N. Wang, Fujita exponent for the global-in time sollutions to a semilinear heat equation with non homogeneous weights, to apper in J. Evol. Equ.
  1. M. Fila, K. Ishige, and T. Kawakami, Solvability of the heat equation on a half-space with a dynamical boundary condition and unbounded initial data, Z. Angew. Math. Phys. 74 (2023), Paper No. 143, 17 pp. impact factor; SJR
  1. K. Ishige and T. Kawakami, Refined asymptotic expansions of solutions to fractional diffusion equations, to apper in J. Dynam. Differential Equations.
  1. S. Hasegawa, N. Ikoma and T. Kawakami, On weak solutions to a fractional Hardy-Henon equation: Part II: Existence, Nonlinear Anal. 227 (2023), Paper No. 113165, 48 pp.
  1. K. Ishige, T. Kawakami and S. Okabe, Existence of solutions to nonlinear parabolic equations via majorant integral kernel, Nonlinear Anal. 223 (2022), Paper No.113025, 22pp.
  1. G. Furioli, T. Kawakami and E. Terraneo, Heat equation with an exponential nonlinear boundary condtion in the half space, Partial Differ. Equ. Appl. 3 (2022), Paper No.36.
  1. S. Hasegawa, N. Ikoma and T. Kawakami, On weak solutions to a fractional Hardy-Henon equation: Part I: Nonexistence. Commun. Pure Appl. Anal. 20 (2021), 1559--1600. impact factor; SJR
  1. M. Fila, K. Ishige, T. Kawakami and J. Lankeit, The large diffusion limit for the heat equation in the exterior of the unit ball with a dynamical boundary condition, Discrete Cintin. Dyn. Syst. 40 (2020), 6529--6546. impact factor; SJR
  1. K. Ishige, T. Kawakami and S. Okabe, Existence of solutions for a higher-order semilinear parabolic equation with singular initial data, Ann. Inst. H. Poincaré Anal. Non Linéaire 37 (2020) 1185--1209. impact factor; SJR
  1. T. Kawakami and M. Muratori, Nonexistence of radial optimal functions for the Sobolev inequality on Mn, to appear in Springer INdAM Series
  1. M. Jleli, T. Kawakami and B. Samet, Critical behavior for a semilinear parabolic equation with forcing term depending of time and space, J. Math. Anal. Appl. 486 (2020), 123931, 16 pp. impact factor; SJR
  1. M. Fila, K. Ishige and T. Kawakami, The large diffusion limit for the heat equation with a dynamical boundary condition, Commun. Contemp. Math. 23 (2021), 2050003, 20 pp. impact factor; SJR
  1. Y. Fujishima, T. Kawakami and Y. Sire, Critical exponent for the global existence of solutions to a semilinear heat equation with degenerate coefficients, Calc. Var. Partial Differential Equations 58 (2019), Art. 62. impact factor; SJR
  1. M. Fila, K. Ishige, T. Kawakami and Johannes Lankeit, Rate of convergence in the large diffusion limit for the heat equation with a dynamical boundary condition, Asymptot. Anal. 114 (2019), 37--57. impact factor; SJR
  1. K. Ishige and T. Kawakami, Critical Fujita exponents for semilinear heat equations with quadratically decaying potential, Indiana Univ. Math. J. 69 (2020) 2171--2207. impact factor; SJR
  1. K. Ishige, T. Kawakami and H. Michihisa, Asymptotic expansions of solutions of fractional diffusion equations, SIAM J. Math. Anal. 49 (2017), 2167--2190. impact factor; SJR
  1. M. Fila, K. Ishige and T. Kawakami, An exterior nonlinear elliptic problem with a dynamical boundary condition, Rev. Mat. Complut. 30 (2017), 281--312. impact factor; SJR
  1. G. Furioli, T. Kawakami, B. Ruf and E. Terraneo, Asymptotic behavior and decay estimates of the solutions for a nonlinear parabolic equation with exponential nonlinearity, J. Differential Equations 262 (2017), 145--180. impact factor; SJR
  1. T. Kawakami and H. Takeda, Higher order asymptotic expansions to the solutions for a nonlinear damped wave equation, No DEA Nonlinear Differential Equations Appl. 23 (2016), Art. 54, 30pp. impact factor; SJR
  1. T. Iwabuchi and T. Kawakami, Existence of mild solutions for the Hamilton-Jacobi equation with critical fractional viscosity in the Besov spaces, J. Math. Pures Appl. 107 (2017), 464--489. impact factor; SJR
  1. K. Ishige, T. Kawakami and M. Sierzega, Supersolutions for a class of nonlinear parabolic systems, J. Differential Equations 260 (2016), 6084--6107. impact factor; SJR
  1. M. Fila, K. Ishige and T. Kawakami, Minimal solutions of a semilinear elliptic equation with a dynamical boundary condition, J. Math. Pures Appl. 105 (2016), 788--809. impact factor; SJR
  1. M. Fila, K. Ishige and T. Kawakami, Positive solutions of a semilinear elliptic equation with singular Dirichelet boundary data, J. Ellipitic Parabol. Equ. 1 (2015), 331--357.
  1. T. Kawakami and Y. Sugiyama, Uniqueness theorem on weak solutions to the Keller-Segel system of degenerate and singular types, J. Differential Equations 260 (2016), 4683--4716. impact factor; SJR
  1. M. Fila, K. Ishige and T. Kawakami, Existence of positive solutions of a semilinear elliptic equation with a dynamical boundary condition, Calc. Var. Partial Differential Equations 54 (2015), 2059--2078. impact factor; SJR
  1. T. Kawakami and S. Sakaguchi, When does the heat equation have a solution with a sequence of similar level sets?, Ann. Mat. Pura Appl. 194 (2015), 1595--1605. impact factor; SJR
  1. K. Ishige, T. Kawakami and K. Kobayashi, Asymptotics for a nonlinear integral equation with a generalized heat kernel, J. Evol. Equ. 14 (2014), 749--777. impact factor; SJR
  1. Y. Kabeya, T. Kawakami, A. Kosaka and H. Ninomiya, Eigenvalues of the Laplace-Beltrami operator on a large spherical cap under the Robin problem, Kodai Math. J. 37 (2014), 620--645. impact factor; SJR
  1. T. Kawakami, Higher order asymptotic expansion for the heat equation with a nonlinear boundary condition, Funkcialaj Ekvacioj 57 (2014), 57--89. impact factor; SJR
  1. K. Ishige, T. Kawakami and K. Kobayashi, Global solutions for a nonlinear integral equation with a generalized heat kernel, Discrete Contin. Dyn. Syst. Ser. S. 7 (2014), 767--783.
  1. M. Fila, K. Ishige and T. Kawakami, Large time behavior of small solutions of a two-dimensional semilinear elliptic equation with a dynamical boundary condition, Asymptot. Anal. 85 (2013), 107--123. impact factor; SJR
  1. K. Ishige and T. Kawakami, Asymptotic expansions of solutions of the Cauchy problem for nonlinear parabolic equations, J. Anal. Math. 121 (2013), 317--351. impact factor; SJR
  1. M. Fila, K. Ishige and T. Kawakami, Large time behavior of solutions of a semilinear elliptic equation with a dynamical boundary condition, Adv. Differential Equations 18 (2013), 69--100. impact factor; SJR
  1. T. Kawakami and Y. Ueda, Asymptotic profiles to the solutions for a nonlinear damped wave equation, Differential Integral Equations 26 (2013), 781--814. impact factor; SJR
  1. K. Ishige and T. Kawakami, Refined asymptotic profiles a semilinear heat equation, Math. Ann. 353 (2012), 161--192. impact factor; SJR
  1. M. Fila, K. Ishige and T. Kawakami, Convergence to the Poisson kernel for the Laplace equation with a nonlinear dynamical boundary condition, Commun. Pure Appl. Anal. 11 (2012), 1285--1301. impact factor; SJR
  1. T. Kawakami, Entropy dissipation method for the solutions of the heat equation with a nonlinear boundary condition, Adv. Math. Sci. Appl. 20 (2010), 169--192.
  1. K. Ishige and T. Kawakami, Global solutions of the heat equation with a nonlinear boundary condition, Calc. Var. Partial Differential Equations 39 (2010), 429--457.impact factor; SJR
  1. T. Kawakami, Global existence of solutions for the heat equation with a nonlinear boundary condition, J. Math. Anal. Appl. 368 (2010), 320--329. impact factor; SJR
  1. K. Ishige, M. Ishiwata and T. Kawakami, The decay of the solutions for the heat equation with a potential, Indiana Univ. Math. J. 58 (2009), 2673--2707. impact factor; SJR
  1. K. Ishige and T. Kawakami, Asymptotic behavior of solutions for some semilinear heat equations in RN, Commun. Pure Appl. Anal. 8 (2009), 1351--1371. impact factor; SJR

Preprint

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  1. Y. Fujishima, K. Ishige and T. Kawakami, Existence of solutions for a semilinear parabolic systemwith singular initial data,
  1. K. Ishige, T. Kawakami and R. Takada Existence of solutions to the fractional semilinear heat equation with a singular inhomogeneous term,
  1. K. Ishige, S. Katayama and T. Kawakami Fundamental solution to the heat equation with a dynamical boundary condition,

Proceeding

  1. T. Kawakami, Entropy dissipations methods for the solutions of the porous medium equation with absorption. Nonlinear phenomena with energy dissipation, 243--252, GAKUTO Internat. Ser. Math. Sci. Appl., 29, Gakkōtosho, Tokyo, 2008.
  1. K. Ishige and T. Kawakami, Asymptotic behavior of solutions of some semilinear heat equations in RN. Recent advances in nonlinear analysis, 171--180, World Sci. Publ., Hackensack, NJ, 2008.

Talk (International conference)

  1. Asymptotic expansions of solutions to fractional diffusion equations, Geometric PDE and Applied Analysis Seminar, OIST, Okinawa, June, 2024.
  1. Existence of solutions to a fractional semilinear heat equation in uniformly local weak Zygmund type spaces, Italian Japanese Nonlinear Days, Milano Univeristy, Milano, Italy, May, 2024.
  1. Existence of solutions to a fractional semilinear heat equation in uniformly local weak Zygmund type spaces, East Asia Workshop on Nonlinear Evolution Equations, The University of Tokyo, Tokyo, March, 2024.
  1. Solvability of the heat equation on a half-space with a dynamical boundary condition, Workshop on Reaction-Diffusion Equations and Related Stochastic Topics, Waseda University, Tokyo, Nobember, 2023.
  1. Solvability of the heat equation on a half-space with a dynamical boundary condition, Euro-Japanese Conference on Nonlinear diffusions, ICMAT-UAM, Madrid, Spain, October, 2023.
  1. Solvability of the heat equation on a half-space with a dynamical boundary condition, Evolution Equations and Related Topics - Energy Structures and Quantitative Analysis -, RIMS, October, 2023.
  • Existence of solutions to nonlinear parabolic equations via majorant integral kernel Seminar on Qualitative Theory of DIfferential Equations, Comenius University, Bratislava, Slovakia, October, 2022.
    1. The large diffusion limit for the heat equation with a dynamical boundary condition, BIRS-CMO Workshop "New Trends in Nonlinear Diffusion: a Bridge between PDEs, Analysis and Geometry", Casa Mathematica Oaxaca (Online), September, 2021.
    1. Critical Fujita exponents for semilinear heat equations with quadratically decaying potential, Nonlinear Analysis Workshop, Chinese academy of Science, October, 2019.
    1. Critical exponent for the global existence of solutions to a semilinear heat equation with degenerate coefficients, New development in the theory of evolution equations: theory, phenomena and technology, RIMS, September, 2019.
    1. Critical exponent for the global existence of solutions to a semilinear heat equation with degenerate coefficients, 4th Swiss-Japanese PDE Seminar, I-site Namba, September, 2019.
    1. Critical exponent for the global existence of solutions to a semilinear heat equation with degenerate coefficients, The 44th Sapporo Symposium on Partial Differential Equations, Hokkaido University, August, 2019.
    1. Critical Fujita exponents for semilinear heat equations with quadratically decaying potential, Workshop on Nonlinear parabolic PDEs and related fields, The University of Tokyo, June, 2019.
    1. The large diffusion limit for the heat equation with a dynamical boundary condition, Vi Italian-Japanese workshop on Geometric Properties for Parabolic and Elliptic PDE's, Cortona, Italy, May, 2019.
    1. The large diffusion limit for the heat equation with a dynamical boundary condition, PDE seminar, East China Normal University, Shanghai, China, May, 2019.
    1. Heat equation with a dynamical boundary condition, 12th AIMS International Conference on Dyn. Systems, Diff. Equations and Applications, National Taiwan University, Taipei, Taiwan, July, 2018.
    1. Positive solutions of a semilinear elliptic equation with singular Dirichlet boundary data, 12th AIMS International Conference on Dyn. Systems, Diff. Equations and Applications, National Taiwan University, Taipei, Taiwan, July, 2018.
    1. Large diffusion limit for the heat equation with a dynamical boundary condition, 8th Euro-Japanses Workshop On Blow-up, Tohoku University, Sendai, Japan June, 2018.
    1. Critical Fujita exponents for semilinear heat equations with quadratically decaying potential, UK-Japan Workshop on Analysis of Nonlinear Partial Differential Equations, Swansea University, Swansea, UK, May, 2018.
    1. A semilinear elliptic equation with a dynamical boundary condition, 1138th AMS Meeting, Special Session on Partuial Differential Equations and New Perspecrive of Variational Methods, Vanderbilt University, Nashville, USA, April, 2018.
    1. A semilinear elliptic equation with a dynamical boundary condition, Seminario di Analisi matematica, University of Bergamo, Dalmine, Italy, November, 2017.
    1. Asymptotic expansion of solutions of fractional diffusion equations, Seminario di Analisi Nonlineare, University of Milano, Milano, Italy, November, 2017.
    1. An exterior nonlinear elliptic problem with a dynamical boundary condition, Analysis and Partial Differential Quations Semionar, Johns Hopkins University, Baltimore, USA, Octorber, 2017.
    1. Decay estimates of the solutions for a nonlinear parabolic equation, Equadiff 2017, Slovak University of Technology in Bratislava, Bratislava, Slovakia, July, 2017.
    1. Asymptotic expansion of solutions of fractional diffusion equations, Singularity and asymptotic behavior os solutions for partial differential equations with conservation law, RIMS, Kyoto, June, 2017.
    1. An exterior nonlinear elliptic problem with a dynamical boundary condition, 2017 NCTS Workshop on Applied Mathematics ant Tainan, NCTS, Tainan University, March, 2017.
    1. Asymptotic behavior and decay estimates of the solutions for a nonlinear parabolic equation with exponential nonlinearity, International Workshop on Nonlinear PDEs 2016 in Osaka, Osaka Prefecture University, Nanba, December, 2016.
    1. An exterior nonlinear elliptic problem with a dynamical boundary condition, Analysis on Shapes of Solutions to Partial Differential Equations, RIMS, Kyoto, November, 2016.
    1. An exterior nonlinear elliptic problem with a dynamical boundary condition, Geometry of solutions of PDE's and its related inverse problems, Tohoku University, Sendai, October, 2016.
    1. A semilinear elliptic equation with a dynamical boundary condition, 7th Euro-Japanese workshop on Blow-up, Bedlewo, Poland, September, 2016.
    1. Minimal solutions of a semilinear elliptic equation with a dynamical boundary condition, XXXVI Convegno di Analisi Armonica,Gargnano, Italy, June, 2016.
    1. Minimal solutions of a semilinear elliptic equation with a dynamical boundary condition, 9th European conference on elliptic and parabolic problems, Gaeta, Italy, May, 2016.
    1. Higher order asymptotic expansions to the solutions for a nonlinear damped wave equation, Qualitative Theory of Differential Equation, Comenius University, Bratislava, Slovakia, May, 2016.
    1. Minimal solutions of a semilinear elliptic equation with a dynamical boundary condition, Seminari d'edps i aplicacions, Universitat Politecnica de Catalunya, Barcelona, Spain, February, 2016.
    1. Existence of mild solutions for the Hamilton-Jacobi equation with critical fractional viscosity in the Besov spaces, Seminario di Calcolo delle Variazioni & Equazioni alle Derivate Parziali, Universita degli Studi di Firenze, Florence, Italy, February, 2016.
    1. Existence of mild solutions for the Hamilton-Jacobi equation with critical fractional viscosity in the Besov spaces, Qualitative Theory of Differential Equation, Comenius University, Bratislava, Slovakia, November, 2015.
    1. Minimal solutions of a semilinear elliptic equation with a dynamical boundary condition, Seminari di Analisi nonlineare, Universita degli studi di Milano, Italia, November 2015.
    1. When does the heat equation have a solution with a sequence of similar level sets?, Geometric Properties for Parabolic and Elliptic PDE's, 4th Italian-Japanese Workshop, Palinuro, Italia, May 2015.
    1. When does the heat equation have a solution with a sequence of similar level sets?, Qualitative Theory of Differential Equation, Comenius University, Bratislava, Slovakia, May, 2015.
    1. When does the heat equation have a solution with a sequence of similar level sets?, 2015 NCTS Workshop on Applied Mathematics, Tankang University, Taiwan, March 2015
    1. When does the heat equation have a solution with a sequence of similar level sets?, Singularities Arising in Nonilinear Problems 2014, Kansai Seminar House, Kyoto, November 2014
    1. Existence of positive solutions of a semilinear elliptic equation with a dynamical boundary condition, HMC seminar, Kanazawa University, Kanazawa, November 2014
    1. Existence of positive solutions of a semilinear elliptic equation with a dynamical boundary condition, 10th AIMS International Conference on Dyn. Systems, Diff. Equations and Applications, Madrid, Spain, July 2014
    1. Existence of positive solutions of a semilinear elliptic equation with a dynamical boundary condition, 8th European conference on elliptic and parabolic problems, Gaeta, Italia, May 2014.
    1. Large time behavior of solutions of a semilinear elliptic equation with a dynamical boundary condition, 3rd Italian-Japanese Workshop on Geometric Properties for Parabolic and Elliptic PDE's, Tokyo Institute of Technology, Tokyo, September 2013.
    1. Large time behavior of solutions of a semilinear elliptic equation with a dynamical boundary condition, Equadiff 13, Prague, Czech Republic, August 2013.
    1. Asymptotic expansions of solutions of the Cauchy problem for nonlinear parabolic equations, ERC-NUMERIWAVES Seminar, BCAM, Spain, March 2013.
    1. Large time behavior of solutions of some elliptic equations with a dynamical boundary condition, Fukae workshop on PDE (2013), Kobe, Japan, January 2013.
    1. Convergence to the Poisson kernel for the Laplace equation with a nonlinear dynamical boundary condition, Swiss-Japanese seminar, Zurich, Switzerland, December 2012.
    1. Higher order asymptotic expansion for the heat equation with a nonlinear boundary condition, 5th Euro-Japanese Workshop on Blow-up, Luminy, France, September 2012.
    1. Convergence to the Poisson kernel for the Laplace equation with a nonlinear dynamical boundary condition,Second Sino-Chilean Conference on Nonlinear Partial Differential Equations and Nonlinear Analysis, Facultad Mathematicas Pontificia Unversidad Catolica, Santiago, July, 2012.
    1. High order asymptotic expansion for the heat equation with a nonlinear boundary condition, Workshop on Nonlinear Partial Differential Equations, Dept of Math Center of PDE, ECNU, November, 2011.
    1. High order asymptotic expansion for the heat equation with a nonlinear boundary condition, Analysis on Non-equilibria and Nonlinear Phenomena -from the evolution equation point of view-, RIMS, Kyoto, October, 2011.
    1. Asymptotic profile for the Laplace equation with a nonlinear dynamical boundary condition, Concentration and Related Topics for Nonlinear Problems, Tohoku University, November, 2010.
    1. Convergence to the Poisson kernel for the Laplace equation with a nonlinear dynamical boundary condition, The 14th Hiroshima Applied Analysis Seminar, Hiroshima University, November, 2010.
    1. Refined asymptotic profiles for a semilinear heat equation, Qualitative Theory of Differential Equation, Comenius University, Bratislava, Slovakia, September, 2010.
    1. Refined asymptotic profiles for a semilinear heat equation, 4th Euro-Japanese Workshop on Blow-up, Lorentz Center, Leiden, Netherlands, September, 2010
    1. On the heat equation in a half-space with a nonlinear boundary condition, The 2nd GCOE International Symposium "Weaving Science Web beyond Particle-Matter Hierarchy", Tohoku University, February, 2010.
    1. On the heat equation in a half space with a nonlinear boundary condition, The second Chile-Japan workshop on nonlinear elliptic and parabolic PDEs, Meiji University, December, 2009.
    1. On the heat equation in a half space with a nonlinear boundary condition, 1st Italian-Japanese workshop on geometric properties for parabolic and elliptic PDE's, Tohoku University, June, 2009.
    1. On the heat equation in a half-space with a nonlinear boundary condition, Variational Problems and Related Topics, RIMS, Kyoto, June, 2009.
    1. Large time behavior of solutions for the heat equation with a nonlinear boundary condition, 2009 NCTS Taiwan-Japan Workshop on Partial Differential Equations, NCTS, Hsinchu, Taiwan, February, 2009.
    1. Entropy dissipations methods for the sign-changing solutions of some semilinear heat equations with the nonlinear boundary condition, Czech-Japanese Seminar in Applied Mathematics 2008, Miyazaki University, September, 2008.
    1. Entropy dissipations methods for the sign-changing solutions of some semilinear heat equations with the nonlinear boundary condition, The 9th Hiroshima Applied Analysis Seminar, Hiroshima University, September, 2008.
    1. Entropy dissipations methods for the sign-changing solutions of heat equations with the nonlinear boundary condition, 7th AIMS International Conference on Dyn. Systems, Diff. Equations and Applications, University of Texas at Arlington, USA, May, 2008.
    1. Entropy dissipations methods for the sign-changing solutions of heat equations with the nonlinear boundary condition, Taiwan-Tohoku Seminar on Differential Equations, Tohoku University, April, 2008.
    1. Entropy dissipations methods for the sign-changing solutions of heat equations with the nonlinear boundary condition, Minnesota-Tohoku seminar on PDE's, University of Minnesota, USA, March, 2008.
    1. Entropy dissipations methods for the sign-changing solutions of heat equations with the nonlinear boundary condition, The 9th Northeastern Symposium on Mathematical Analysis, Hokkaido University, February, 2008.
    1. Asymptotic behavior of solutions for some semilinear heat equations in RN, International Conference on Free boundary Problems in Chiba, Chiba University, November, 2007.
    1. Asymptotic behavior of solutions for some semilinear heat equations in RN, Equadiff 2007, Vienna University of Technology, Vienna, Austria, August, 2007.
    1. Asymptotic behavior of solutions for some semilinear heat equations, The 8th Northeastern Symposium on Mathematical Analysis, Tohoku University, February, 2007.
    1. Asymptotic Behavior of Solutions for Some Semilinear Heat Equation in RN, NCTS 2006 International Conference on Nonlinear Analysis, NCTS, Hsinchu, Taiwan, November, 2006.

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