Organization
Faculty of Advanced Engineering
Department
Regional ICT Research Center for Human, Industry and Future
Title
Associate Professor
External link
SUGIYAMA Yusuke
Degree
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博士（理学） ( 2013.3 東京理科大学 )
Research Field
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Blow-up
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Quasilinear wave equations
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Hyperbolic conservation law
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Partial differential equations
Research Experience
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The University of Shiga Prefecture Regional ICT Research Center for Human, Industry and Future Associate Professor
2020.4
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The University of Shiga Prefecture School of Engineering Department of Electronic Systems Engineering Associate Professor
2018.3 - 2020.3
Association Memberships
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日本数学会
2011.4
Research Areas
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Natural Science / Mathematical analysis
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Natural Science / Basic mathematics / 偏微分方程式
Available Technology
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物理現象を記述する偏微分方程式の数学解析
Papers
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Local solvability for a quasilinear wave equation with the far field degeneracy: 1D case Reviewed International journal
Yuusuke Sugiyama
Communications in Mathematical Sciences 21 219 - 237 2023.1
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Formation of singularities for a family of 1D quasilinear wave equations Reviewed International journal
Yuusuke Sugiyama
Indiana University Mathematical Journal 71 2529 - 2549 2022.12
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Asymptotic stability of stationary solutions to the drift-diffusion model with the fractional dissipation Reviewed
Sugiyama Y., Yamamoto M.
Journal of Evolution Equations 21 ( 2 ) 1383 - 1417 2021.6
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Optimal estimates for far field asymptotics of solutions to the quasi-geostrophic equation Reviewed International journal
Masakazu Yamamoto, Yuusuke Sugiyama
Proceedings of the American Mathematical Society 149 1099 - 1110 2021.1
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Remark on global existence of solutions to the 1D compressible Euler equation with time-dependent damping Reviewed International journal
Yuusuke Sugiyama
Advanced Studies in Pure Mathematics 85 379 - 389 2021.1
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Spatial-decay of solutions to the quasi-geostrophic equation with the critical and the supercritical dissipation Reviewed International journal
山本征法, 杉山裕介
Nonlinearity 32 2467 - 2480 2019.5
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Singularity formation for the 1D compressible Euler equations with variable damping coefficient Reviewed International journal
Yuusuke Sugiyama
Nonlinear Analysis Series A: Theory, Methods & Applications 170 70 - 87 2018
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Existence and nonexistence theorems for global weak solutions to quasilinear wave equations for the elasticity Reviewed International journal
Yunguang Lu, Yuusuke Sugiyama
Applied Mathematics Letters 2018
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Large time behavior of solutions to 1D quasilinear wave equations Reviewed
Yuusuke Sugiyama
RIMS Kokyuroku Bessatsu, B63 113 - 123 2017
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Degeneracy in finite time of 1D quasilinear wave equations II Reviewed
Yuusuke Sugiyama
Evolution Equations and Control Theory 6 ( 615 ) 628 2017
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Asymptotic behavior of solutions to the drift-diffusion equation with critical dissipation Reviewed International journal
Yamamoto Masakazu, Yuusuke Sugiyama
Annales Henri Poincare 17 1331 - 1352 2016
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Asymptotic expansion of solutions to the drift-diffusion equation with fractional dissipatio Reviewed International journal
Yamamoto Masakazu, Yuusuke Sugiyama
Nonlinear Analysis Series A: Theory, Methods & Applications 141 ( 57 ) 87 2016
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Degeneracy in finite time of 1D quasilinear wave equations Reviewed International journal
Yuusuke Sugiyama
SIAM J. Math. Anal. 48 ( 847 ) 860 2016
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Local and global solvability and blow up for the drift-diffusion equation with fractional dissipation in the critical space Reviewed International journal
Yuusuke Sugiyama, Yamamoto Masakazu, Keiichi Kato
Journal of Differential Equations 258 2983 - 3010 2015
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Existence and analyticity of solutions to the drift-diffusion equation with critical dissipation Reviewed International journal
Yamamoto Masakazu, Keiichi Kato, Yuusuke Sugiyama
Hiroshima Mathematical Journal 44 275 - 313 2014
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Blow up of solutions to the second sound equation in one space dimension Reviewed
Keiichi Kato, Yuusuke Sugiyama
Kyushu journal of mathematics 67 126 - 142 2013
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Global existence of solutions to some quasilinear wave equation in one space dimension Reviewed International journal
Yuusuke Sugiyama
Differential and integral equations 26 487 - 504 2013
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Local existence and uniqueness theory for the second sound equation in one space dimension Reviewed International journal
Keiichi Kato, Yuusuke Sugiyama
Journal of hyperbolic differential equations 9 177 - 193 2012
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Nonexistence of global solution to some quasilinear hyperbolic equation Reviewed International journal
Yuusuke Sugiyama
SUT journal of mathematics 47 217 - 227 2011
Research Projects
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退化型準線形波動方程式における正則性理論の深化と未解決問題への応用
2023.4 - 2027.3
基盤研究(C)
Grant type：Competitive
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退化型準線形波動方程式の正則性理論の構築とその応用
2019.4 - 2022.3
日本学術振興会 若手研究
杉山裕介
Grant amount：\2900000 （ Direct Cost: \2900000 ）
主要部が未知関数に依存する準線形波動方程式においては、未知関数が大きく振動し、方程式の主要部の係数が0へと近づき（方程式が退化し）、波動方程式として構造を崩すことがある。本研究ではまず、elastic systemと呼ばれる空間1次元双曲型保存則系を取り扱い、退化する点付近の解の正則性理論を構築し、その応用として未解決問題「古典解及び弱解の時間大域存在」の解決を目指す。その後、高次元化、高階化（システム化）などを含むような一般論構築を目指す。
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退化型準線形波動方程式の解の挙動の分類
2016.4 - 2019.3
若手研究B
杉山裕介
Grant amount：\2210000 （ Direct Cost: \1700000 、 Indirect Cost：\510000 ）
Presentations
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Formation of singularities for the 1D compressible Euler equation with time and spacedependent damping Invited
杉山裕介
Saga Workshop on Partial Differential Equations 2023.3
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変数係数摩擦項を持つ 1 次元圧縮性オイラー方程式の時間大域解の存在 Invited
杉山裕介
偏微分方程式の解の特異性とその周辺 2023.1
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On the self-similar solution to the 1D drift-diffusion equation with the half-Laplacian
杉山裕介、山本征法
黒木場正城教授 追悼研究集会「非線型偏微分方程式と走化性」 2022.11
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変数係数摩擦項を持つ１次元圧縮性オイラー方程式に関する注意 Invited
杉山裕介
The Second One Day Workshop on Hyperbolic PDE in Kushiro 2022.11
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ある１次元準線形波動方程式の解の爆発 International conference
杉山裕介
大阪大学微分方程式セミナー 2022.5
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Local solvability for a quasilinear wave equation with the far files degeneracy Invited International conference
Yuusuke Sugiyama
Online Seminar on Hyperbolic PDEs 2021.11
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Formation of singularities for1D quasilinear wave equations, Invited International conference
Yuusuke Sugiyama
Online Seminar on Hyperbolic PDEs 2021.5
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Formation of singularities for a family of 1D quasilinear wave equations Invited International conference
Yuusuke Sugiyama
wave seminar 2021.1
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Finite time blow-up for parameterized 1D quasilinear wave equations
Yuusuke Sugiyama
日本数学会秋季総合分科会 2020.9
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Asymptotic stability of stationary solutions to the drift-diffusion model with the fractional dissipation Invited
山本征法
楕円型・放物型微分方程式研究集会 2019.11
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Stationary and nonstationary problems for the drift-diffusion equation with fractional dissipation Invited International conference
山本征法
Chemotaxis and Nonlinear Parabolic Equations 2019.11
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Existence and stability of stationary solutions to the drift-diffusion equation with the fractional dissipation Invited
杉山裕介, 山本征法
RIMS共同研究「反応拡散方程式と非線形分散型方程式の解の挙動 」 2019.2 京都大学数理解析研究所
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Loss of strict hyperbolicity in finite time for 1D quasilinear wave equations Invited
杉山裕介
ＮＬＰＤＥセミナー 2018.12
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分数冪ラプラシアンを持つ移流拡散方程式の可解性や解の長時間挙動を支えるいくつかの評価について Invited
杉山裕介
解析学研究セミナー 2018.12 熊本大学
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Remark on global existence and large time behavior for the 1D Euler equation with time-dependent damping Invited
杉山裕介
南大阪応用数学セミナー 2018.11
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準地衡近似方程式の解の空間遠方での減衰について
山本征法, 杉山裕介
日本数学会秋季総合分科会 2018.9
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Global existence and degeneracy in finite time for 1D quasilinear wave equations Invited International conference
杉山裕介
国際研究集会「MSJ-SI」 The 11th Mathematical Society of Japan (MSJ) Seasonal Institute (SI) The Role of Metrics in the Theory of Partial Differential Equations 2018.7
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Large time behavior of solutions to 1D quasilinear wave equations for the elasticity Invited
杉山裕介
熊本大学応用解析セミナー 2018.6 熊本大学
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Global existence and degeneracy in finite time for 1D quasilinear wave equations Invited
杉山裕介
微分方程式セミナー 2018.6
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Degeneracy in finite time for 1D quasilinear wave equations Invited
杉山裕介
大阪駅前セミナー 2018.1
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Existence and nonexistence theorems for global weak solutions to quasilinear wave equations Invited
杉山裕介
Okayama Workshop on Partial Differential Equations 2017.10
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Singularity formation for the 1D compressible Euler equation with variable damping coefficient Invited
杉山裕介
The 15th Linear and Nonlinear Waves 2017.10