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Dissipativity for a semi-linearized system modeling cellular flames
1. | Department of Mathematical Sciences, IUPUI, Indianapolis, IN 46202-3216, United States |
2. | Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180-3590 |
3. | School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel |
References:
[1] |
C.-M. Brauner and A. Lunardi, Instabilities in a two-dimensional combustion model with free boundary,, Arch. Rational. Mech. Anal., 154 (2000), 157.
doi: doi:10.1007/s002050000099. |
[2] |
C.-M. Brauner, M. Frankel, J. Hulshof and G. I. Sivashinsky, Weakly nonlinear asymptotics of the $\kappa-\theta$ model of cellular flames: The QS equation,, Interfaces Free Bound., 7 (2005), 131.
doi: doi:10.4171/IFB/117. |
[3] |
C.-M. Brauner, M. Frankel, J. Hulshof and V. Roytburd, Stability and attractors for the quasi-steady equation of cellular flames,, Interfaces Free Bound., 8 (2006), 301.
doi: doi:10.4171/IFB/145. |
[4] |
C.-M. Brauner, M. Frankel, J. Hulshof, A. Lunardy and G. I. Sivashinsky, On the model of cellular flames: Existence in the large and asymptotics,, DCDS-S, 1 (2008), 27.
|
[5] |
C. Foias and G. Prodi, Sur le comportement global des solutions non stationnaire des équations Navier-Stokes en dimension 2,, Rend. Sem. Mat. Univ. Padova, 39 (1967), 1.
|
[6] |
M. L. Frankel and G. I. Sivashinsky, On the nonlinear thermal-diffusive theory of curved flames,, J. Physique, 48 (1987), 25. Google Scholar |
[7] |
M. Frankel, P. V. Gordon and G. I. Sivashinsky, On disintegration of near-limit cellular flames,, Phys. Lett. A, 310 (2003), 389.
doi: doi:10.1016/S0375-9601(03)00385-2. |
[8] |
M. Frankel and V.Roytburd, Numerical study of the semi-linearized system modeling cellular flames,, In preparation (2009)., (2009). Google Scholar |
[9] |
J. Goodman, Stability of the Kuramoto-Sivashinsky and related systems,, Comm. Pure Appl. Math., 47 (1994), 293.
doi: doi:10.1002/cpa.3160470304. |
[10] |
D. Henry, "Geometric Theory of Semilinear Parabolic Equations,", Lecture Notes in Mathematics, 840 (1981).
|
[11] |
D. Hilhorst, L. A. Peletier, A. I. Rotariu and G. I. Sivashinsky, Global attractor and inertial sets for a non-local Kuramoto-Sivashinsky equation,, DCDS-A, 10 (2004), 557. Google Scholar |
[12] |
Y. Kuramoto, Diffusion induced chaos in reactions systems,, Progr. Theoret. Phys. Suppl., 64 (1978), 346.
doi: doi:10.1143/PTPS.64.346. |
[13] |
B. Malomed, Bao-Feng Feng and T. Kawahara, Stabilized Kuramoto-Sivashinsky system,, Phys. Rev. E, 64 (2001). Google Scholar |
[14] |
B. J. Matkowsky and G. I. Sivashinsky, An asymptotic derivation of two models in flame theory associated with the constant density approximation,, SIAM J. Appl. Math., 37 (1979), 696.
doi: doi:10.1137/0137051. |
[15] |
A. A. Nepomnyashchy, Stability of wave regimes in a film flowing down on inclined plane,, Fluid Dyn., 9 (1974), 354.
doi: doi:10.1007/BF01025515. |
[16] |
G. I. Sivashinsky, Nonlinear analysis of hydrodynamic instability in laminar flames, Part I. Derivation of basic equations,, Acta Astronaut. 4 (1977), 4 (1977), 1177.
doi: doi:10.1016/0094-5765(77)90096-0. |
[17] |
R. Temam, "Infinite-Dimensional Dynamical Systems in Mechanics and Physics," 2nd edition,, Springer-Verlag, (1997).
|
[18] |
J. Topper and T. Kawahara, Approximate equations for long nonlinear waves on a viscous film,, J. Phys. Soc. Japan, 44 (1978), 663.
doi: doi:10.1143/JPSJ.44.663. |
show all references
References:
[1] |
C.-M. Brauner and A. Lunardi, Instabilities in a two-dimensional combustion model with free boundary,, Arch. Rational. Mech. Anal., 154 (2000), 157.
doi: doi:10.1007/s002050000099. |
[2] |
C.-M. Brauner, M. Frankel, J. Hulshof and G. I. Sivashinsky, Weakly nonlinear asymptotics of the $\kappa-\theta$ model of cellular flames: The QS equation,, Interfaces Free Bound., 7 (2005), 131.
doi: doi:10.4171/IFB/117. |
[3] |
C.-M. Brauner, M. Frankel, J. Hulshof and V. Roytburd, Stability and attractors for the quasi-steady equation of cellular flames,, Interfaces Free Bound., 8 (2006), 301.
doi: doi:10.4171/IFB/145. |
[4] |
C.-M. Brauner, M. Frankel, J. Hulshof, A. Lunardy and G. I. Sivashinsky, On the model of cellular flames: Existence in the large and asymptotics,, DCDS-S, 1 (2008), 27.
|
[5] |
C. Foias and G. Prodi, Sur le comportement global des solutions non stationnaire des équations Navier-Stokes en dimension 2,, Rend. Sem. Mat. Univ. Padova, 39 (1967), 1.
|
[6] |
M. L. Frankel and G. I. Sivashinsky, On the nonlinear thermal-diffusive theory of curved flames,, J. Physique, 48 (1987), 25. Google Scholar |
[7] |
M. Frankel, P. V. Gordon and G. I. Sivashinsky, On disintegration of near-limit cellular flames,, Phys. Lett. A, 310 (2003), 389.
doi: doi:10.1016/S0375-9601(03)00385-2. |
[8] |
M. Frankel and V.Roytburd, Numerical study of the semi-linearized system modeling cellular flames,, In preparation (2009)., (2009). Google Scholar |
[9] |
J. Goodman, Stability of the Kuramoto-Sivashinsky and related systems,, Comm. Pure Appl. Math., 47 (1994), 293.
doi: doi:10.1002/cpa.3160470304. |
[10] |
D. Henry, "Geometric Theory of Semilinear Parabolic Equations,", Lecture Notes in Mathematics, 840 (1981).
|
[11] |
D. Hilhorst, L. A. Peletier, A. I. Rotariu and G. I. Sivashinsky, Global attractor and inertial sets for a non-local Kuramoto-Sivashinsky equation,, DCDS-A, 10 (2004), 557. Google Scholar |
[12] |
Y. Kuramoto, Diffusion induced chaos in reactions systems,, Progr. Theoret. Phys. Suppl., 64 (1978), 346.
doi: doi:10.1143/PTPS.64.346. |
[13] |
B. Malomed, Bao-Feng Feng and T. Kawahara, Stabilized Kuramoto-Sivashinsky system,, Phys. Rev. E, 64 (2001). Google Scholar |
[14] |
B. J. Matkowsky and G. I. Sivashinsky, An asymptotic derivation of two models in flame theory associated with the constant density approximation,, SIAM J. Appl. Math., 37 (1979), 696.
doi: doi:10.1137/0137051. |
[15] |
A. A. Nepomnyashchy, Stability of wave regimes in a film flowing down on inclined plane,, Fluid Dyn., 9 (1974), 354.
doi: doi:10.1007/BF01025515. |
[16] |
G. I. Sivashinsky, Nonlinear analysis of hydrodynamic instability in laminar flames, Part I. Derivation of basic equations,, Acta Astronaut. 4 (1977), 4 (1977), 1177.
doi: doi:10.1016/0094-5765(77)90096-0. |
[17] |
R. Temam, "Infinite-Dimensional Dynamical Systems in Mechanics and Physics," 2nd edition,, Springer-Verlag, (1997).
|
[18] |
J. Topper and T. Kawahara, Approximate equations for long nonlinear waves on a viscous film,, J. Phys. Soc. Japan, 44 (1978), 663.
doi: doi:10.1143/JPSJ.44.663. |
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