Reseach

Publication

1. Sugiyama, Yuusuke, Nonexistence of global solution to some second order quasilinear hyperbolic equation, SUT Journal of Mathematics 47, no. 2, 217--227, 2011

2. Kato, Keiichi; Sugiyama, Yuusuke, Local existence and uniqueness theory for the second sound equation in one space dimension, Journal of Hyperbolic Differential Equations 9, no. 1, 177--193, 2012.

3. Kato, Keiichi; Sugiyama, Yuusuke, Blow up of solutions to the second sound equation in one space dimension, Kyushu Journal of Mathematics 67, no. 1, 129--142, 2013.

4. Sugiyama, Yuusuke, Global existence of solutions to some quasilinear wave equation in one space dimension, Differential and Integral Equations 26, no. 5-6, 487--504, 2013.

5. Yamamoto, Masakazu; Kato, Keiichi; Sugiyama, Yuusuke, Existence and analyticity of solutions to the drift-diffusion equation with critical dissipation, Hiroshima Mathematical Journal 44, no. 3, 275--313, 2014.

6. Sugiyama, Yuusuke; Yamamoto, Masakazu; Kato, Keiichi, Local and global solvability and blow up for the drift-diffusion equation with the fractional dissipation in the critical space, Journal of Differential Equations 258, no. 9, 2983--3010, 2015.

7. Sugiyama, Yuusuke, Degeneracy in finite time of 1D quasilinear wave equations, SIAM Journal on Mathematical Analysis 48, no. 2, 847--860, 2016.

8. Yamamoto, Masakazu; Sugiyama, Yuusuke, Asymptotic behavior of solutions to the drift-diffusion equation with critical dissipation, Annales Henri Poincaré 17, no. 6, 1331--1352, 2016.

9. Yamamoto, Masakazu; Sugiyama, Yuusuke, Asymptotic expansion of solutions to the drift-diffusion equation with fractional dissipation, Nonlinear Analysis 141, 57--87, 2016.

10. Sugiyama, Yuusuke, Degeneracy in finite time of 1D quasilinear wave equations. II., Evolution Equations and Control Theory 6, no. 4, 615--628, 2017.

11. Sugiyama, Yuusuke, Large time behavior of solutions to 1D quasilinear wave equations, RIMS Kôkyûroku Bessatsu B63, 115--125, 2017.

12. Sugiyama, Yuusuke, Singularity formation for the 1D compressible Euler equations with variable damping coefficient, Nonlinear Analysis 170, 70--87, 2018.

13. Lu, Yun-Guang; Sugiyama, Yuusuke, Existence and nonexistence theorems of global weak solutions to degenerate quasilinear wave equations for the elasticity, Applied Mathematics Letters 84, 118--123, 2018.

14. Yamamoto, Masakazu; Sugiyama, Yuusuke, Spatial-decay of solutions to the quasi-geostrophic equation with the critical and supercritical dissipation, Nonlinearity 32, no. 7, 2467--2480, 2019.

15. Yamamoto, Masakazu; Sugiyama, Yuusuke, Optimal estimates for far field asymptotics of solutions to the quasi-geostrophic equation, Proceedings of the American Mathematical Society 149, no. 3, 1099--1110, 2021.

16. Sugiyama, Yuusuke, Remark on global existence of solutions to the 1D compressible Euler equation with time-dependent damping, in Advanced Studies in Pure Mathematics 85, 379--389, 2021.

17. Sugiyama, Yuusuke; Yamamoto, Masakazu, Asymptotic stability of stationary solutions to the drift-diffusion model with the fractional dissipation, Journal of Evolution Equations 21, no. 2, 1383--1417, 2021.

18. Sugiyama, Yuusuke, Formation of singularities for a family of 1D quasilinear wave equations, Indiana University Mathematics Journal 71, no. 6, 2529--2549, 2022.

19. Sugiyama, Yuusuke, Local solvability for a quasilinear wave equation with the far field degeneracy: 1D case, Communications in Mathematical Sciences 21, no. 1, 219--237, 2023.

20. Hu, Yanbo; Sugiyama, Yuusuke, The classical solvability for a one-dimensional nonlinear thermoelasticity system with the far field degeneracy, Advances in Nonlinear Studies 24, no. 4, 857--879, 2024.

21. Sugiyama, Yuusuke, Global existence and blow-up for the 1D damped compressible Euler equations with time and space dependent perturbation, Nonlinear Analysis 250, Article ID 113658, 2025.

22. Hu, Yanbo; Sugiyama, Yuusuke, Well-posedness of the initial-boundary value problem for 1D degenerate quasilinear wave equations, Advances in Differential Equations 30, no. 3-4, 177--206, 2025.

23. Hu, Yanbo; Sugiyama, Yuusuke, Well-posedness of degenerate initial-boundary value problems to a hyperbolic-parabolic coupled system arising from nematic liquid crystals, Archive for Rational Mechanics and Analysis 249, no. 2, Paper No. 19, 2025. 

Preprint

Yanbo Hu, Yuusuke Sugiyama, Loss of regularity for solutions to 1D degenerate quasilinear wave equations

Kanai, Takumi; Muramatsu, Ryo; Sugiyama, Yuusuke, Wave front set of solutions to the fractional Schrödinger equation, preprint, 2026. arXiv:2602.17406

Yuusuke Sugiyama, Global well-posedness for a one-dimensional quasilinear wave equation, arXiv:2605.01814.

Yuusuke Sugiyama, Tato Yamanoi,  Lifespan of Classical Solutions to One-Dimensional Quasilinear Wave Equations, arXiv:2605.04976.

arXiv:2602.17406