Stability in a two-dimensional free boundary combustion model

Nonlinear Analysis, Theory, Methods and Applications

Volumn 53, Issue 2, 2003, Pages 227-276

  Lorenzi, Luca ^a   Lunardi, Alessandra ^a  

^a UNIVERSITY OF PARMA   (Italy)

Author keywords

Free boundary problems; Fully nonlinear parabolic problems; Stability of travelling waves

Indexed keywords

COMBUSTION; LINEARIZATION; MATHEMATICAL MODELS; NONLINEAR SYSTEMS; PROBLEM SOLVING;

FREE BOUNDARY PROBLEMS;

BOUNDARY VALUE PROBLEMS;

EID: 0037392995     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(02)00289-4     Document Type: Article

References (19)

1. Agmon S., Douglis A., Nirenberg L. Estimates near the boundary for solutions to elliptic partial differential equations satisfying general boundary conditions II. Commun. Pure Appl. Math. 17:1964;35-92.
2. Alabau F., Lunardi A. Behaviour near the travelling wave solution of a free boundary system in Combustion Theory. Dyn. Syst. Appl. 1:1992;391-418.
3. Baconneau O., Lunardi A. Smooth solutions to a class of free boundary parabolic problems. Dipart. Mat. Univ. Parma. 253:2001;. preprint, submitted for publication.
4. Brauner C.-M., Hulshof J., Lunardi A. A general approach to stability in free boundary problems. J. Differential Equations. 164:2000;16-48.
5. Brauner C.-M., Hulshof J., Lunardi A. A critical case of stability in a free boundary problem. J. Evolutionary Equations. 1:2001;85-113.
6. Brauner C.-M., Lunardi A. Instabilities in a two-dimensional combustion model with free boundary. Arch. Ration. Mech. Anal. 154:2000;157-182.
7. Buckmaster J.D., Ludford G.S.S. Theory of Laminar Flames. 1982;Cambridge University Press, Cambridge.
8. J.D. Buckmaster, G.S.S. Ludford, Lectures on mathematical combustion, CBMS-NSF Conference series Applied Mathematics, SIAM, Philadelphia, PA, 1983.
9. A. Erdélyi, W. Magnus, F. Oberhettinger, F.G. Tricomi, Tables of Integral Transforms, Vol. 1, Mc Graw-Hill Book Company, New York, 1954.
10. L. Lorenzi, Regularity and analyticity in a two-dimensional combustion model, Differential Integral Equations, to appear.
11. L. Lorenzi, A free boundary problem stemmed from combustion theory. Part I: existence, uniqueness and regularity results, J. Math. Anal. Appl., to appear.
12. L. Lorenzi, A free boundary problem stemmed from combustion theory. Part II: stability, instability and bifurcation results, J. Math. Anal. Appl., to appear.
13. Lunardi A. Analytic Semigroups and Optimal Regularity in Parabolic Problems. 1995;Birkhäuser, Basel.
14. Margolis S.B., Sivashinsky G.I. Flame propagation in vertical channels. bifurcation to bimodal cellular flames SIAM J. Appl. Math. 44:1983;344-368.
15. Matkowski B.J., Sivashinsky G.I. An asymptotic derivation of two models in flame theory associated with the constant density approximation. SIAM J. Appl. Math. 37:1979;686-699.
16. Michelson D.M., Sivashinsky G.I. Nonlinear analysis of hydrodynamics instability in laminar flames - II. Numerical experiments. Acta Astronaut. 4:1977;1207-1221.
17. Sinestrari E. On the abstract Cauchy problem of parabolic type in spaces of continuous functions. J. Math. Anal. Appl. 107:1985;16-66.
18. Sivashinsky G.I. Nonlinear analysis of hydrodynamics instability in laminar flames - I. Derivation of basic equations. Acta Astronaut. 4:1977;1177-1206.
19. Sivashinsky G.I. On flame propagation under conditions of stoichiometry. SIAM J. Appl. Math. 39:1980;67-82.