American Institute of Mathematical Sciences

Advanced
2003, 2003(Special): 916-925. doi: 10.3934/proc.2003.2003.916

Boundary conditions for multi-dimensional hyperbolic relaxation problems

Wen-Qing Xu 1,

1. 

Department of Mathematics, California State University, Long Beach, CA 90840

Received  September 2002 Revised  March 2003 Published  April 2003

We study the IBVP for a class of linear relaxation systems in a half space with arbitrary space dimensions. The goal is to determine the appropriate structural stability conditions, particularly, the formulation of boundary conditions such that the relaxation IBVP is stiffly well-posed or uniformly well-posed independent of the relaxation parameter. Our main contribution is the derivation, in an explicit and easily checkable form, of a stiff version of the classical Uniform Kreiss Condition (and hence referred to as Stiff Kreiss Condition). The Stiff Kreiss Condition is shown to be necessary and su±cient for the stiff well-posedness of the relaxation IBVP and its asymptotic convergence to the underlying equilibrium system in the zero relaxation limit.
Keywords: stiff Kreiss condition, conservation laws, uniform Kreiss condition, subcharacteristic condition, zero relaxation limit, boundary layers..
Mathematics Subject Classification: Primary: 35L50; Secondary: 35B25, 35B35, 35L6.
Citation: Wen-Qing Xu. Boundary conditions for multi-dimensional hyperbolic relaxation problems. Conference Publications, 2003, 2003 (Special) : 916-925. doi: 10.3934/proc.2003.2003.916
[1]

Alberto Bressan, Marta Lewicka. A uniqueness condition for hyperbolic systems of conservation laws. Discrete & Continuous Dynamical Systems, 2000, 6 (3) : 673-682. doi: 10.3934/dcds.2000.6.673
[2]

Evgeny Yu. Panov. On a condition of strong precompactness and the decay of periodic entropy solutions to scalar conservation laws. Networks & Heterogeneous Media, 2016, 11 (2) : 349-367. doi: 10.3934/nhm.2016.11.349
[3]

Khadijah Sharaf. A perturbation result for a critical elliptic equation with zero Dirichlet boundary condition. Discrete & Continuous Dynamical Systems, 2017, 37 (3) : 1691-1706. doi: 10.3934/dcds.2017070
[4]

Ming Mei, Yau Shu Wong, Liping Liu. Phase transitions in a coupled viscoelastic system with periodic initial-boundary condition: (I) Existence and uniform boundedness. Discrete & Continuous Dynamical Systems - B, 2007, 7 (4) : 825-837. doi: 10.3934/dcdsb.2007.7.825
[5]

Marek Fila, Kazuhiro Ishige, Tatsuki Kawakami, Johannes Lankeit. The large diffusion limit for the heat equation in the exterior of the unit ball with a dynamical boundary condition. Discrete & Continuous Dynamical Systems, 2020, 40 (11) : 6529-6546. doi: 10.3934/dcds.2020289
[6]

Lan Zeng, Guoxi Ni, Yingying Li. Low Mach number limit of strong solutions for 3-D full compressible MHD equations with Dirichlet boundary condition. Discrete & Continuous Dynamical Systems - B, 2019, 24 (10) : 5503-5522. doi: 10.3934/dcdsb.2019068
[7]

R.G. Duran, J.I. Etcheverry, J.D. Rossi. Numerical approximation of a parabolic problem with a nonlinear boundary condition. Discrete & Continuous Dynamical Systems, 1998, 4 (3) : 497-506. doi: 10.3934/dcds.1998.4.497
[8]

Samia Challal, Abdeslem Lyaghfouri. The heterogeneous dam problem with leaky boundary condition. Communications on Pure & Applied Analysis, 2011, 10 (1) : 93-125. doi: 10.3934/cpaa.2011.10.93
[9]

Nicolas Van Goethem. The Frank tensor as a boundary condition in intrinsic linearized elasticity. Journal of Geometric Mechanics, 2016, 8 (4) : 391-411. doi: 10.3934/jgm.2016013
[10]

H. Beirão da Veiga. Vorticity and regularity for flows under the Navier boundary condition. Communications on Pure & Applied Analysis, 2006, 5 (4) : 907-918. doi: 10.3934/cpaa.2006.5.907
[11]

Wenzhen Gan, Peng Zhou. A revisit to the diffusive logistic model with free boundary condition. Discrete & Continuous Dynamical Systems - B, 2016, 21 (3) : 837-847. doi: 10.3934/dcdsb.2016.21.837
[12]

Jean-François Coulombel, Frédéric Lagoutière. The Neumann numerical boundary condition for transport equations. Kinetic & Related Models, 2020, 13 (1) : 1-32. doi: 10.3934/krm.2020001
[13]

Raffaela Capitanelli. Robin boundary condition on scale irregular fractals. Communications on Pure & Applied Analysis, 2010, 9 (5) : 1221-1234. doi: 10.3934/cpaa.2010.9.1221
[14]

Jesús Ildefonso Díaz, L. Tello. On a climate model with a dynamic nonlinear diffusive boundary condition. Discrete & Continuous Dynamical Systems - S, 2008, 1 (2) : 253-262. doi: 10.3934/dcdss.2008.1.253
[15]

M. Eller. On boundary regularity of solutions to Maxwell's equations with a homogeneous conservative boundary condition. Discrete & Continuous Dynamical Systems - S, 2009, 2 (3) : 473-481. doi: 10.3934/dcdss.2009.2.473
[16]

Christina A. Hollon, Jeffrey T. Neugebauer. Positive solutions of a fractional boundary value problem with a fractional derivative boundary condition. Conference Publications, 2015, 2015 (special) : 615-620. doi: 10.3934/proc.2015.0615
[17]

K. T. Joseph, Philippe G. LeFloch. Boundary layers in weak solutions of hyperbolic conservation laws II. self-similar vanishing diffusion limits. Communications on Pure & Applied Analysis, 2002, 1 (1) : 51-76. doi: 10.3934/cpaa.2002.1.51
[18]

Hongyun Peng, Lizhi Ruan, Changjiang Zhu. Convergence rates of zero diffusion limit on large amplitude solution to a conservation laws arising in chemotaxis. Kinetic & Related Models, 2012, 5 (3) : 563-581. doi: 10.3934/krm.2012.5.563
[19]

Qi An, Chuncheng Wang, Hao Wang. Analysis of a spatial memory model with nonlocal maturation delay and hostile boundary condition. Discrete & Continuous Dynamical Systems, 2020, 40 (10) : 5845-5868. doi: 10.3934/dcds.2020249
[20]

Yizhuo Wang, Shangjiang Guo. A SIS reaction-diffusion model with a free boundary condition and nonhomogeneous coefficients. Discrete & Continuous Dynamical Systems - B, 2019, 24 (4) : 1627-1652. doi: 10.3934/dcdsb.2018223

 Impact Factor: 

Tools

Metrics

  • PDF downloads (26)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences