
Previous Article
An agestructured twosex model in the space of radon measures: Well posedness
 KRM Home
 This Issue

Next Article
Coupling of nonlocal driving behaviour with fundamental diagrams
Convergence rates towards the traveling waves for a model system of radiating gas with discontinuities
1.  Research Institute of Nonlinear Partial Differential Equations, Organization for University Research Initiatives, Waseda University, 341 Ohkubo Shinjuku, Tokyo 1698555, Japan 
References:
[1] 
R. Duan, K. Fellner and C. Zhu, Energy method for multidimensional balance laws with nonlocal dissipation, J. Math. Pures Appl., 93 (2010), 572598. doi: 10.1016/j.matpur.2009.10.007. 
[2] 
W. Gao, L. Ruan and C. Zhu, Decay rates to the planar rarefaction waves for a model system of the radiating gas in $n$ dimensions J. Differential Equations, 244 (2008), 26142640. doi: 10.1016/j.jde.2008.02.023. 
[3] 
K. Hamer, Nonlinear effects on the propagation of sounds waves in a radiating gas, Quarter J. Mech. Appl. Math., 24 (1971), 155168. doi: 10.1093/qjmam/24.2.155. 
[4] 
S. Kawashima and A. Matsumura, Asymptotic stability of traveling wave solutions of systems for onedimensional gas motion, Comm. Math. Phys., 101 (1985), 97127. doi: 10.1007/BF01212358. 
[5] 
S. Kawashima and S. Nishibata, Weak solutions with a shock to a model system of the radiating gas, Sci. Bull. Josai Univ. special issue, 5 (1998), 119130. 
[6] 
S. Kawashima and S. Nishibata, Shock waves for a model system of the radiating gas, SIAM J. Math. Anal., 30 (1999), 95117. doi: 10.1137/S0036141097322169. 
[7] 
S. Kawashima and S. Nishibata, Cauchy problem for a model system of the radiating gas: Weak solutions with a jump and classical solutions, Math. Models. Meth. Sci., 9 (1999), 6991. 
[8] 
S. Kawashima, S. Nishibata and P. Zhu, Asymptotic stability of the stationary solution to the compressible NavierStokes equations in the half space, Comm. Math. Phys., 240 (2003), 483500. 
[9] 
S. Kawashima and Y. Tanaka, Stability of rarefaction waves for a model system of radiating gas, Kyushu J. Math., 58 (2004), 211250. doi: 10.2206/kyushujm.58.211. 
[10] 
S. N. Kruzkov, First order quasilinear equations in several independent variables, Math. USSR Sbor., 10 (1970), 217243. doi: 10.1070/SM1970v010n02ABEH002156. 
[11] 
C. Lattanzio, C. Mascia, T. Nguyen, R. Plaza and K. Zumbrun, Stability of scalar radiative shock profiles, SIAM J. Math. Anal., 41 (2009), 21652206. doi: 10.1137/09076026X. 
[12] 
A. Matsumura and K. Nishihara, Asymptotic stability of traveling waves for scalar viscous conservation laws with nonconvex nonlinearity, Commun. Math. Phys., 165 (1994), 8396. doi: 10.1007/BF02099739. 
[13] 
S. Nishibata, Asymptotic behavior of solutions to a model system of radiating gas with discontinuous initial data, Math. Models. Meth. Appl. Sci., 8 (2000), 12091231. 
[14] 
M. Nishikawa, Convergence rate to the traveling wave for viscous conservation laws, Funkcialaj Ekvacioj, 41 (1998), 107132. 
[15] 
M. Nishikawa and S. Nishibata, Convergence rates toward the traveling waves for a model system of the radiating gas, Math. Meth. Appl. Sci., 30 (2007), 649663. doi: 10.1002/mma.800. 
[16] 
D. Serre, $L^1$stability of constants in a model for radiating gases, Comm. Math. Sci., 1 (2003), 197205. 
[17] 
M. Suzuki, Asymptotic stability of stationary solutions to the EulerPoisson equations arising in plasma physics, Kinetic Related Models, 4 (2011), 569588. 
[18] 
W. Wang and W. Wang, The pointwise estimates of solutions for a model system of the radiating gas in multidimensions, Nonlinear Anal., 71 (2009), 11801195. doi: 10.1016/j.na.2008.11.050. 
show all references
References:
[1] 
R. Duan, K. Fellner and C. Zhu, Energy method for multidimensional balance laws with nonlocal dissipation, J. Math. Pures Appl., 93 (2010), 572598. doi: 10.1016/j.matpur.2009.10.007. 
[2] 
W. Gao, L. Ruan and C. Zhu, Decay rates to the planar rarefaction waves for a model system of the radiating gas in $n$ dimensions J. Differential Equations, 244 (2008), 26142640. doi: 10.1016/j.jde.2008.02.023. 
[3] 
K. Hamer, Nonlinear effects on the propagation of sounds waves in a radiating gas, Quarter J. Mech. Appl. Math., 24 (1971), 155168. doi: 10.1093/qjmam/24.2.155. 
[4] 
S. Kawashima and A. Matsumura, Asymptotic stability of traveling wave solutions of systems for onedimensional gas motion, Comm. Math. Phys., 101 (1985), 97127. doi: 10.1007/BF01212358. 
[5] 
S. Kawashima and S. Nishibata, Weak solutions with a shock to a model system of the radiating gas, Sci. Bull. Josai Univ. special issue, 5 (1998), 119130. 
[6] 
S. Kawashima and S. Nishibata, Shock waves for a model system of the radiating gas, SIAM J. Math. Anal., 30 (1999), 95117. doi: 10.1137/S0036141097322169. 
[7] 
S. Kawashima and S. Nishibata, Cauchy problem for a model system of the radiating gas: Weak solutions with a jump and classical solutions, Math. Models. Meth. Sci., 9 (1999), 6991. 
[8] 
S. Kawashima, S. Nishibata and P. Zhu, Asymptotic stability of the stationary solution to the compressible NavierStokes equations in the half space, Comm. Math. Phys., 240 (2003), 483500. 
[9] 
S. Kawashima and Y. Tanaka, Stability of rarefaction waves for a model system of radiating gas, Kyushu J. Math., 58 (2004), 211250. doi: 10.2206/kyushujm.58.211. 
[10] 
S. N. Kruzkov, First order quasilinear equations in several independent variables, Math. USSR Sbor., 10 (1970), 217243. doi: 10.1070/SM1970v010n02ABEH002156. 
[11] 
C. Lattanzio, C. Mascia, T. Nguyen, R. Plaza and K. Zumbrun, Stability of scalar radiative shock profiles, SIAM J. Math. Anal., 41 (2009), 21652206. doi: 10.1137/09076026X. 
[12] 
A. Matsumura and K. Nishihara, Asymptotic stability of traveling waves for scalar viscous conservation laws with nonconvex nonlinearity, Commun. Math. Phys., 165 (1994), 8396. doi: 10.1007/BF02099739. 
[13] 
S. Nishibata, Asymptotic behavior of solutions to a model system of radiating gas with discontinuous initial data, Math. Models. Meth. Appl. Sci., 8 (2000), 12091231. 
[14] 
M. Nishikawa, Convergence rate to the traveling wave for viscous conservation laws, Funkcialaj Ekvacioj, 41 (1998), 107132. 
[15] 
M. Nishikawa and S. Nishibata, Convergence rates toward the traveling waves for a model system of the radiating gas, Math. Meth. Appl. Sci., 30 (2007), 649663. doi: 10.1002/mma.800. 
[16] 
D. Serre, $L^1$stability of constants in a model for radiating gases, Comm. Math. Sci., 1 (2003), 197205. 
[17] 
M. Suzuki, Asymptotic stability of stationary solutions to the EulerPoisson equations arising in plasma physics, Kinetic Related Models, 4 (2011), 569588. 
[18] 
W. Wang and W. Wang, The pointwise estimates of solutions for a model system of the radiating gas in multidimensions, Nonlinear Anal., 71 (2009), 11801195. doi: 10.1016/j.na.2008.11.050. 
[1] 
N. V. Chemetov. Nonlinear hyperbolicelliptic systems in the bounded domain. Communications on Pure and Applied Analysis, 2011, 10 (4) : 10791096. doi: 10.3934/cpaa.2011.10.1079 
[2] 
Gervy Marie Angeles, Gilbert Peralta. Energy method for exponential stability of coupled onedimensional hyperbolic PDEODE systems. Evolution Equations and Control Theory, 2022, 11 (1) : 199224. doi: 10.3934/eect.2020108 
[3] 
Steinar Evje, Kenneth H. Karlsen. Hyperbolicelliptic models for wellreservoir flow. Networks and Heterogeneous Media, 2006, 1 (4) : 639673. doi: 10.3934/nhm.2006.1.639 
[4] 
Yan Cui, Zhiqiang Wang. Asymptotic stability of wave equations coupled by velocities. Mathematical Control and Related Fields, 2016, 6 (3) : 429446. doi: 10.3934/mcrf.2016010 
[5] 
SunHo Choi. Weighted energy method and long wave short wave decomposition on the linearized compressible NavierStokes equation. Networks and Heterogeneous Media, 2013, 8 (2) : 465479. doi: 10.3934/nhm.2013.8.465 
[6] 
Giuseppe Floridia, Hiroshi Takase, Masahiro Yamamoto. A Carleman estimate and an energy method for a firstorder symmetric hyperbolic system. Inverse Problems and Imaging, , () : . doi: 10.3934/ipi.2022016 
[7] 
Kaifang Liu, Lunji Song, Shan Zhao. A new overpenalized weak galerkin method. Part Ⅰ: Secondorder elliptic problems. Discrete and Continuous Dynamical Systems  B, 2021, 26 (5) : 24112428. doi: 10.3934/dcdsb.2020184 
[8] 
Lunji Song, Wenya Qi, Kaifang Liu, Qingxian Gu. A new overpenalized weak galerkin finite element method. Part Ⅱ: Elliptic interface problems. Discrete and Continuous Dynamical Systems  B, 2021, 26 (5) : 25812598. doi: 10.3934/dcdsb.2020196 
[9] 
Kenta Nakamura, Tohru Nakamura, Shuichi Kawashima. Asymptotic stability of rarefaction waves for a hyperbolic system of balance laws. Kinetic and Related Models, 2019, 12 (4) : 923944. doi: 10.3934/krm.2019035 
[10] 
Yulan Lu, Minghui Song, Mingzhu Liu. Convergence rate and stability of the splitstep theta method for stochastic differential equations with piecewise continuous arguments. Discrete and Continuous Dynamical Systems  B, 2019, 24 (2) : 695717. doi: 10.3934/dcdsb.2018203 
[11] 
Florian Monteghetti, Ghislain Haine, Denis Matignon. Asymptotic stability of the multidimensional wave equation coupled with classes of positivereal impedance boundary conditions. Mathematical Control and Related Fields, 2019, 9 (4) : 759791. doi: 10.3934/mcrf.2019049 
[12] 
Jinyan Fan, Jianyu Pan. On the convergence rate of the inexact LevenbergMarquardt method. Journal of Industrial and Management Optimization, 2011, 7 (1) : 199210. doi: 10.3934/jimo.2011.7.199 
[13] 
Yves Bourgault, Damien Broizat, PierreEmmanuel Jabin. Convergence rate for the method of moments with linear closure relations. Kinetic and Related Models, 2015, 8 (1) : 127. doi: 10.3934/krm.2015.8.1 
[14] 
Denis Serre, Alexis F. Vasseur. The relative entropy method for the stability of intermediate shock waves; the rich case. Discrete and Continuous Dynamical Systems, 2016, 36 (8) : 45694577. doi: 10.3934/dcds.2016.36.4569 
[15] 
Kazuhiro Kurata, Yuki Osada. Asymptotic expansion of the ground state energy for nonlinear Schrödinger system with three wave interaction. Communications on Pure and Applied Analysis, 2021, 20 (12) : 42394251. doi: 10.3934/cpaa.2021157 
[16] 
Yichen Zhang, Meiqiang Feng. A coupled $ p $Laplacian elliptic system: Existence, uniqueness and asymptotic behavior. Electronic Research Archive, 2020, 28 (4) : 14191438. doi: 10.3934/era.2020075 
[17] 
George Avalos, Roberto Triggiani. Semigroup wellposedness in the energy space of a parabolichyperbolic coupled StokesLamé PDE system of fluidstructure interaction. Discrete and Continuous Dynamical Systems  S, 2009, 2 (3) : 417447. doi: 10.3934/dcdss.2009.2.417 
[18] 
Jiequn Han, Jihao Long. Convergence of the deep BSDE method for coupled FBSDEs. Probability, Uncertainty and Quantitative Risk, 2020, 5 (0) : 5. doi: 10.1186/s4154602000047w 
[19] 
Haibo Cui, Zhensheng Gao, Haiyan Yin, Peixing Zhang. Stationary waves to the twofluid nonisentropic NavierStokesPoisson system in a half line: Existence, stability and convergence rate. Discrete and Continuous Dynamical Systems, 2016, 36 (9) : 48394870. doi: 10.3934/dcds.2016009 
[20] 
Per Christian Moan, Jitse Niesen. On an asymptotic method for computing the modified energy for symplectic methods. Discrete and Continuous Dynamical Systems, 2014, 34 (3) : 11051120. doi: 10.3934/dcds.2014.34.1105 
2020 Impact Factor: 1.432
Tools
Metrics
Other articles
by authors
[Back to Top]