May  2001, 1(2): 193-208. doi: 10.3934/dcdsb.2001.1.193

Existence of travelling wave solutions in a combustion-radiation model

1. 

Department of Mathematical Analysis, Free University, De Boelelaan 1081, 1081 HV Amsterdam, Netherlands

2. 

Université Bordeaux I, Mathématiques Appliquées de Bordeaux, 33405 Talence Cedex, France

3. 

CEA-CESTA, BP 2, 33114 Le Barp Cedex, France

Received  November 2000 Revised  January 2001 Published  February 2001

We consider a simple model of premixed flames propagating in a gaseous mixture containing inert dust. The radiation field is modelled by the classical Eddington equation. The main parameters are the dimensionless opacity and the Boltzmann number. We prove the existence of travelling solutions with increased speed w.r.t. the adiabatic case. Several singular limiting cases (including a modification involving an ignition temperature) of the parameter values are discussed.
Citation: Claude-Michael Brauner, Josephus Hulshof, J.-F. Ripoll. Existence of travelling wave solutions in a combustion-radiation model. Discrete and Continuous Dynamical Systems - B, 2001, 1 (2) : 193-208. doi: 10.3934/dcdsb.2001.1.193
[1]

Josephus Hulshof, Pascal Noble. Travelling waves for a combustion model coupled with hyperbolic radiation moment models. Discrete and Continuous Dynamical Systems - B, 2008, 10 (1) : 73-90. doi: 10.3934/dcdsb.2008.10.73

[2]

Claude-Michel Brauner, Josephus Hulshof, Luca Lorenzi, Gregory I. Sivashinsky. A fully nonlinear equation for the flame front in a quasi-steady combustion model. Discrete and Continuous Dynamical Systems, 2010, 27 (4) : 1415-1446. doi: 10.3934/dcds.2010.27.1415

[3]

Claude-Michel Brauner, Luca Lorenzi. Instability of free interfaces in premixed flame propagation. Discrete and Continuous Dynamical Systems - S, 2021, 14 (2) : 575-596. doi: 10.3934/dcdss.2020363

[4]

Aníbal Rodríguez-Bernal, Enrique Zuazua. Parabolic singular limit of a wave equation with localized boundary damping. Discrete and Continuous Dynamical Systems, 1995, 1 (3) : 303-346. doi: 10.3934/dcds.1995.1.303

[5]

A. Ducrot. Travelling wave solutions for a scalar age-structured equation. Discrete and Continuous Dynamical Systems - B, 2007, 7 (2) : 251-273. doi: 10.3934/dcdsb.2007.7.251

[6]

Christopher K. R. T. Jones, Robert Marangell. The spectrum of travelling wave solutions to the Sine-Gordon equation. Discrete and Continuous Dynamical Systems - S, 2012, 5 (5) : 925-937. doi: 10.3934/dcdss.2012.5.925

[7]

Giuseppe Maria Coclite, Lorenzo di Ruvo. A singular limit problem for the Ibragimov-Shabat equation. Discrete and Continuous Dynamical Systems - S, 2016, 9 (3) : 661-673. doi: 10.3934/dcdss.2016020

[8]

Wei Wang, Yan Lv. Limit behavior of nonlinear stochastic wave equations with singular perturbation. Discrete and Continuous Dynamical Systems - B, 2010, 13 (1) : 175-193. doi: 10.3934/dcdsb.2010.13.175

[9]

Guy V. Norton, Robert D. Purrington. The Westervelt equation with a causal propagation operator coupled to the bioheat equation.. Evolution Equations and Control Theory, 2016, 5 (3) : 449-461. doi: 10.3934/eect.2016013

[10]

Mudassar Imran, Youssef Raffoul, Muhammad Usman, Chi Zhang. A study of bifurcation parameters in travelling wave solutions of a damped forced Korteweg de Vries-Kuramoto Sivashinsky type equation. Discrete and Continuous Dynamical Systems - S, 2018, 11 (4) : 691-705. doi: 10.3934/dcdss.2018043

[11]

Min Li, Zhaoyang Yin. Blow-up phenomena and travelling wave solutions to the periodic integrable dispersive Hunter-Saxton equation. Discrete and Continuous Dynamical Systems, 2017, 37 (12) : 6471-6485. doi: 10.3934/dcds.2017280

[12]

Borys Alvarez-Samaniego, Pascal Azerad. Existence of travelling-wave solutions and local well-posedness of the Fowler equation. Discrete and Continuous Dynamical Systems - B, 2009, 12 (4) : 671-692. doi: 10.3934/dcdsb.2009.12.671

[13]

Tiberiu Harko, Man Kwong Mak. Travelling wave solutions of the reaction-diffusion mathematical model of glioblastoma growth: An Abel equation based approach. Mathematical Biosciences & Engineering, 2015, 12 (1) : 41-69. doi: 10.3934/mbe.2015.12.41

[14]

John Guckenheimer, Christian Kuehn. Homoclinic orbits of the FitzHugh-Nagumo equation: The singular-limit. Discrete and Continuous Dynamical Systems - S, 2009, 2 (4) : 851-872. doi: 10.3934/dcdss.2009.2.851

[15]

Mohammad Hassan Farshbaf-Shaker, Takeshi Fukao, Noriaki Yamazaki. Singular limit of Allen--Cahn equation with constraint and its Lagrange multiplier. Conference Publications, 2015, 2015 (special) : 418-427. doi: 10.3934/proc.2015.0418

[16]

John R. King, Judith Pérez-Velázquez, H.M. Byrne. Singular travelling waves in a model for tumour encapsulation. Discrete and Continuous Dynamical Systems, 2009, 25 (1) : 195-230. doi: 10.3934/dcds.2009.25.195

[17]

Aiyong Chen, Chi Zhang, Wentao Huang. Limit speed of traveling wave solutions for the perturbed generalized KdV equation. Discrete and Continuous Dynamical Systems - S, 2022  doi: 10.3934/dcdss.2022048

[18]

H. A. Erbay, S. Erbay, A. Erkip. The Camassa-Holm equation as the long-wave limit of the improved Boussinesq equation and of a class of nonlocal wave equations. Discrete and Continuous Dynamical Systems, 2016, 36 (11) : 6101-6116. doi: 10.3934/dcds.2016066

[19]

Seongyeon Kim, Yehyun Kwon, Ihyeok Seo. Strichartz estimates and local regularity for the elastic wave equation with singular potentials. Discrete and Continuous Dynamical Systems, 2021, 41 (4) : 1897-1911. doi: 10.3934/dcds.2020344

[20]

Alhabib Moumni, Jawad Salhi. Exact controllability for a degenerate and singular wave equation with moving boundary. Numerical Algebra, Control and Optimization, 2022  doi: 10.3934/naco.2022001

2020 Impact Factor: 1.327

Metrics

  • PDF downloads (58)
  • HTML views (0)
  • Cited by (1)

[Back to Top]