Preprints
S. Sakata, Y. Wakasugi, Asymptotic properties of a subordinated heat flow and their generalization, submitted.
M. A. Hamza, Y. Wakasugi, S. Yoshikawa, Asymptotic profiles for the Cauchy problem of semilinear beam equation with two variable coefficients in the subcritical case, arXiv:2605.00550v2.
M. Sobajima, K. Tsutaya, Y. Wakasugi, Appearance of Strauss-type exponent in semilinear wave equations with time-dependent speed of propagation, arXiv:2412.08834v1.
Accepted Papers
K. Tsutaya, Y. Wakasugi, Blow up of solutions of semilinear wave equations with time-dependent propagation speed and damping, to appear in: Advanced Studies in Pure Mathematics.
Published Papers
H. Kozono, Y. Terasawa, Y. Wakasugi, Asymptotic behavior of solutions to elliptic equations in 2D exterior domains, Math. Z 313 (2026), no. 2, Paper No. 21, 15pp.
M. Ikeda, T. Inui, Y. Wakasugi, Existence of solutions to the semilinear damped wave equation with non-L2 slowly decaying data : polynomial nonlinearity case, J. Evol. Equ. 26, 37 (2026). https://doi.org/10.1007/s00028-025-01180-9
K. Tsutaya, Y. Wakasugi, Existence of solutions of semilinear wave equations with time-dependent propagation speed and time derivative nonlinearity, Math. Methods Appl. Sci., https://doi.org/10.1002/mma.70493
Y. Wakasugi, Revisit on global existence of solutions for semilinear damped wave equations in R^N with noncompactly supported initial data, in: Ebert, M.R., Kähler, U., Sabadini, I., Toft, J. (eds) New Tools in Mathematical Analysis and Applications. ISAAC 2023. Trends in Mathematics(). Birkhäuser, Cham. (2025).
M. Ikeda, M. Sobajima, K. Taniguchi, Y. Wakasugi, Lifespan estimates for semilinear damped wave equation in a two-dimensional exterior domain, Calc. Var. 63, 240 (2024).
K. Tsutaya, Y. Wakasugi, Remarks on blow up of solutions of nonlinear wave equations in Friedmann-Lemaitre-Robertson-Walker spacetime, In: Machihara, S. (eds) Mathematical Physics and Its Interactions. ICMPI 2021. Springer Proceedings in Mathematics & Statistics, vol 451. Springer, Singapore.
M. A. Hamza, Y. Wakasugi, S. Yoshikawa, Asymptotic profiles for the Cauchy problem of damped beam equation with two variable coefficients and derivative nonlinearity, Discrete and Continuous Dynamical Systems 44 (2024), 2280--2308.
H. Kozono, Y. Terasawa, Y. Wakasugi, Liouville-type theorems for the Taylor--Couette--Poiseuille flow of the stationary Navier--Stokes equations, Journal of Fluid Mechanics, 989 (2024), A7.
M. Ikeda, K. Taniguchi, Y. Wakasugi, Global existence and asymptotic behavior for nonlinear damped wave equations on measure spaces, Evolution Equations and Control Theory 13 (2024), 1101--1125.
M. Sobajima, Y. Wakasugi, Asymptotic expansion of solutions to the wave equation with space-dependent damping, Asymptotic Analysis 134 (2023), 241--279.
H. Kozono, Y. Terasawa, Y. Wakasugi, Asymptotic behavior and Liouville-type theorems for axisymmetric stationary Navier-Stokes equations outside of an infinite cylinder with a periodic boundary condition, J. Differential Equations 365 (2023), 905--926.
Y. Wakasugi, Decay property of solutions to the wave equation with space-dependent damping, absorbing nonlinearity, and polynomially decaying data, Math. Meth. Appl. Sci., https://doi.org/10.1002/mma.8957.
H. Kozono, Y. Terasawa and Y. Wakasugi, Asymptotic properties of steady and nonsteady solutions to the 2d Navier-Stokes equations with finite generalized Dirichlet integral, Indiana Univ. Math. J. 71 (2022), 1299--1316.
K. Tsutaya, Y. Wakasugi, Blow up of solutions of semilinear wave equations in de Sitter spacetime, Partial Differ. Equ. Appl. 3, 6 (2022), 10p.
K. Tsutaya, Y. Wakasugi, Blow up of solutions of semilinear wave equations in accelerated expanding Friedmann-Lemaître-Robertson-Walker spacetime, Reviews in Mathematical Physics 33 (2022), 2250003, 16p.
H. Kozono, Y. Terasawa, Y. Wakasugi, Asymptotic properties of steady solutions to the 3D axisymmetric Navier-Stokes equations with no swirl, J. Funct. Anal. 282 (2022), 109289, 21p.
T. Inui, Y. Wakasugi, Unconditional well-posedness for the energy critical nonlinear damped wave equation, J. Evol. Equ. 21 (2021), 5171--5201.
K. Tsutaya, Y. Wakasugi, On Glassey’s conjecture for semilinear wave equations in Friedmann-Lemaître-Robertson-Walker spacetime, Bound. Value Probl. 2021, 94 (2021), 30p.
M. Sobajima, Y. Wakasugi, Supersolutions for parabolic equations with unbounded or degenerate diffusion and its applications to some classes of parabolic and hyperbolic equations, J. Math. Soc. Japan 73 (2021), 1091--1128.
K. Fujiwara, M. Ikeda, Y. Wakasugi, The Cauchy problem of the semilinear second order evolution equation with fractional Laplacian and damping, Nonlinear Differ. Equ. Appl. 28, 63 (2021), 40p.
A. Umeda, Y. Wakasugi, S. Yoshikawa, Energy-conserving finite difference schemes for nonlinear wave equations with dynamic boundary conditions, Applied Numerical Mathematics 171 (2022), 1--22.
H. Kozono, Y. Terasawa, Y. Wakasugi, Asymptotic behavior of solutions to elliptic and parabolic equations with unbounded coefficients of the second order in unbounded domains, Math. Ann. 380 (2021), 1105--1117.
M. Sobajima, Y. Wakasugi, Remark on one dimensional semilinear damped wave equation in a critical weighted $L^2$-space, in: VI Italian-Japanese workshop on GPPEPDEs, Cortona 2019 - Proceedings, 291--305.
K. Tsutaya, Y. Wakasugi, On heatlike lifespan of solutions of semilinear wave equations in Friedmann-Lemaître-Robertson-Walker spacetime, J. Math. Anal. Appl. 500 (2021), 125133.
S. Yoshikawa, Y. Wakasugi, Classification of asymptotic profiles for the Cauchy problem of damped beam equation with two variable coefficients: effective damping case, J. Differential Equations, 272 (2021), 938--957.
K. Tsutaya, Y. Wakasugi, Blow-up of solutions of semilinear wave equations in Friedmann-Lemaître-Robertson-Walker spacetime, J. Math. Phys., 61, 091503 (2020).
K. Fujiwara, M. Ikeda,Y. Wakasugi, Lifespan of solutions for a weakly coupled system of semilinear heat equations, Tokyo J. Math., 43 (2020), 163--180.
S. Sakata, Y. Wakasugi, Movement of time-delayed hot spots in Euclidean space for special initial states, Discrete Contin. Dyn. Syst. 40 (2020), 2705--2738.
M. Ikeda, Y. Wakasugi, Global well-posedness for the semilinear wave equation with time dependent damping in the overdamping case, Proc. Amer. Math. Soc. 148 (2020), no.1, 157--172.
Y. Wakasugi, Second order asymptotic expansion for wave equations with time- dependent dissipation in one-space dimension, in: Advanced Studies in Pure Mathematics 81 (2019), Asymptotic Analysis for Nonlinear Dispersive and Wave Equations, 401--419.
M. Ikeda, M. Sobajima, Y. Wakasugi, Sharp lifespan estimates of blowup solutions to semilinear wave equations with time-dependent effective damping, J. Hyperbolic Differ. Equ. 16 (2019), no.3, 495--517.
M. Sobajima, Y. Wakasugi, Weighted energy estimates for wave equation with space-dependent damping term for slowly decaying initial data, Commun. Contemp. Math. 21 (2019), no.5, 185035, 30pp.
K. Fujiwara, M. Ikeda, Y. Wakasugi, Estimates of lifespan and blow-up rates for the wave equation with a time-depndent damping and a power-type nonlinearity, Funkcial. Ekvac. 62 (2019), no.2, 157--189.
Y. Wakasugi, A remark on the critical exponent for the semilinear damped wave equation on the half-space, in: the Proceedings of the 11th ISAAC Congress, Växjö(Sweden) 2017, Analysis, Probability, Applications, and Computation, Birkhäuser, 2019.
M. Ikeda, T. Inui, M. Okamoto, Y. Wakasugi, Lp-Lq estimates for the damped wave equation and the critical exponent for the nonlinear problem with slowly decaying data, Comm. Pure Appl. Anal., 18 (2019), 1967--2008.
K. Nishihara, M. Sobajima, Y. Wakasugi, Critical exponent for the semilinear wave equations with a damping increasing in the far field, NoDEA, Nonlinear Differ. Equ. Appl., 25 (2018), no. 6, 25:55.
H. Kozono, Y. Terasawa, Y. Wakasugi, Finite energy for the Navier-Stokes equations and Liouville-type theorems in two dimensional domains, J. Differential Equations 265 (2018), 1227--1247.
M. Sobajima, Y. Wakasugi, Diffusion phenomena for the wave equation with space-dependent damping term growing at infinity, Advances in Differential Equations 23 (2018), 581--614.
S. Yoshikawa, Y. Wakasugi, Asymptotic profile of solution for the Cauchy problem of beam equation with variable coefficient, Appl. Math. Lett. 76 (2018), 236--241.
K. Fujiwara, M. Ikeda, Y. Wakasugi, Blow-up of solutions for weakly coupled systems of complex Ginzburg-Landau Equations, Electronic Journal of Differential Equations 2017 (2017), No.196, 1--16.
Y. Wakasugi, A note on the blow-up of solutions to Nakao’s problem, in: New Trends in Analysis and Interdisciplinary Applications, Selected Contributions of the 10th ISAAC Congress, Macau, Springer Proceedings in Mathematics & Statistics, pp. 545--551.
S. Sakata, Y. Wakasugi, Movement of time-delayed hot spots in Euclidean space, Math. Z. 285 (2017), 1007--1040.
M. Ikeda, T. Inui, Y. Wakasugi, The Cauchy problem for the nonlinear damped wave equation with slowly decaying data, NoDEA, Nonlinear Differ. Equ. Appl. (2017), 24:10.
M. Sobajima, Y. Wakasugi, Remarks on an elliptic problem arising in weighted energy estimates for wave equation with space-dependent damping term in an exterior domain, AIMS Mathematics, 2017, 2(1): 1--15.
H. Kozono, Y. Terasawa, Y. Wakasugi, A Remark on Liouville-type theorems for the stationary Navier-Stokes equations in three space dimensions, J. Funct. Anal. 272 (2017), 804--818.
Journal PDF
Y. Wakasugi, Scaling variables and asymptotic profiles of solutions to the semilinear damped wave equation with variable coefficients, J. Math. Anal. Appl. 447 (2017), 452--487.
M. Sobajima, Y. Wakasugi, Diffusion phenomena for the wave equation with space-dependent damping in an exterior domain, J. Differential Equations 261 (2016), 5690--5718.
K. Nishihara, Y. Wakasugi, Critical exponents for the Cauchy problem to the system of wave equations with time or space dependent damping, Bull. Inst. Math. Acad. Sin. (N.S.) 10 (2015), 283--309.
K. Nishihara, Y. Wakasugi, Global existence of solutions for a weakly coupled system of semilinear damped wave equations, J. Differential Equations 259 (2015), 4172--4201.
M. Ikeda, Y. Wakasugi, A note on the lifespan of solutions to the semilinear damped wave equation, Proc. Amer. Math. Soc. 143 (2015), 163--171.
Y. Wakasugi, On diffusion phenomena for the linear wave equation with space-dependent damping, J. Hyperbolic Diff. Equ. 11 (2014), 795--819.
K. Nishihara, Y. Wakasugi, Critical exponent for the Cauchy problem to the weakly coupled damped wave system, Nonlinear Anal. 108 (2014), 249--259.
Y. Wakasugi, Blow-up of solutions to the one-dimensional semilinear wave equation with damping depending on time and space variables, Discrete Contin. Dyn. Syst. 34 (2014), 3831--3846.
Y. Wakasugi, Critical exponent for the semilinear wave equation with scale invariant damping, in: Fourier Analysis (M. Ruzhansky and V. Turunen, eds.), Trends in Mathematics, Birkh ̈auser, Basel, 2014, 375--390.
M. Ikeda, Y. Wakasugi, Small data blow-up of L2-solution for the nonlinear Schrödinger equation without gauge invariance, Differential Integral Equations, 26 (2013), 1275--1285.
Y. Wakasugi, Small data global existence for the semilinear wave equation with space-time dependent damping, J. Math. Anal. Appl. 393 (2012), 66--79.
Y. Wakasugi, Some examples causing energy growth for solutions to wave equations, Proc. Japan Acad., Ser. A, 87 (2011), 136--141.
Non-Refereed Papers
H. Kozono, Y. Terasawa, Y. Wakasugi, Liouville‐type theorems for the stationary and nonstationary Navier‐Stokes equations, in: The structure of function spaces and its environment, RIMS, Kokyuroku, 2041 (2017), 112--121.
Y. Wakasugi, Asymptotic profiles of solutions to the semilinear wave equation with time-dependent damping, in: Developments of the theory of evolution equations as the applications to the analysis for nonlinear phenomena, RIMS, Kokyuroku, 1997 (2016), 140--155.
K. Nishihara, Y. Wakasugi Critical exponent for the Cauchy problem to the weakly coupled damped wave system, in: Regularity and Singularity for Partial Differential Equations with Conservation Laws, RIMS, Kokyuroku, 1962 (2015), 59--67.