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Global gradient estimates for $p(x)$-Laplace equation in non-smooth domains
S-shaped bifurcation curves for a combustion problem with general arrhenius reaction-rate laws
1. | Department of Mathematics, National Tsing Hua University, Hsinchu 300, Taiwan |
2. | Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan 300 |
3. | Fundamental General Education Center, National Chin-Yi University of Technology, Taichung 411, Taiwan |
References:
[1] |
T. Boddington, C.-G. Feng and P. Gray, Disappearance of criticality in thermal explosion under Frank-Kamenetskii boundary conditions,, \emph{Combust. Flame}, 48 (1982), 303. Google Scholar |
[2] |
T. Boddington, C.-G. Feng and P. Gray, Thermal explosion, criticality and the disappearance of criticality in systems with distributed temperatures. I. Arbitrary Biot number and general reaction-rate laws,, \emph{Proc. R. Soc. Lond. A}, 390 (1983), 247. Google Scholar |
[3] |
T. Boddington, C.-G. Feng and P. Gray, Thermal explosion and the theory of its initiation by steady intense light,, \emph{Proc. R. Soc. Lond. A}, 390 (1983), 265. Google Scholar |
[4] |
T. Boddington, P. Gray and C. Robinson, Thermal explosion and the disappearance of criticality at small activation energies: exact results for the slab,, \emph{Proc. R. Soc. Lond. A}, 368 (1979), 441. Google Scholar |
[5] |
M. G. Crandall and P. H. Rabinowitz, Bifurcation, perturbation of simple eigenvalues and linearized stability,, \emph{Arch. Rational Mech. Anal.}, 52 (1973), 161.
|
[6] |
Y. Du, Exact multiplicity and S-shaped bifurcation curve for some semilinear elliptic problems from combustion theory,, \emph{SIAM J. Math. Anal.}, 32 (2000), 707.
doi: 10.1137/S0036141098343586. |
[7] |
K.-C. Hung and S.-H. Wang, A theorem on S-shaped bifurcation curve for a positone problem with convex-concave nonlinearity and its applications to the perturbed Gelfand problem,, \emph{J. Differential Equations}, 251 (2011), 223.
doi: 10.1016/j.jde.2011.03.017. |
[8] |
P. Korman and Y. Li, On the exactness of an S-shaped bifurcation curve,, \emph{Proc. Amer. Math. Soc.}, 127 (1999), 1011.
doi: 10.1090/S0002-9939-99-04928-X. |
[9] |
G. P. Miller, The structure of a stoichiometric CCI4-CH4-air flat flame,, \emph{Combust. Flame}, 101 (1995), 101. Google Scholar |
[10] |
M. Mimura and K. Sakamoto, Multi-dimensional transition layers for an exothermic reaction-diffusion system in long cylindrical domains,, \emph{J. Math. Sci. Univ. Tokyo}, 3 (1996), 109.
|
[11] |
A. L. Sánchez, A. Liñán and F. A. Williams, Chain-branching explosions in mixing layers,, \emph{SIAM J. Appl. Math.}, 59 (1999), 1335.
doi: 10.1137/S003613999732648X. |
[12] |
K. Taira, Semilinear elliptic boundary-value problems in combustion theory,, \emph{Proc. Roy. Soc. Edinburgh Sect. A}, 132 (2002), 1453.
|
[13] |
S.-H. Wang, On S-shaped bifurcation curves,, \emph{Nonlinear Anal.}, 22 (1994), 1475.
doi: 10.1016/0362-546X(94)90183-X. |
[14] |
S.-H. Wang, Rigorous analysis and estimates of S-shaped bifurcation curves in a combustion problem with general Arrhenius reaction-rate laws,, \emph{Proc. R. Soc. Lond. A}, 454 (1998), 1031. Google Scholar |
show all references
References:
[1] |
T. Boddington, C.-G. Feng and P. Gray, Disappearance of criticality in thermal explosion under Frank-Kamenetskii boundary conditions,, \emph{Combust. Flame}, 48 (1982), 303. Google Scholar |
[2] |
T. Boddington, C.-G. Feng and P. Gray, Thermal explosion, criticality and the disappearance of criticality in systems with distributed temperatures. I. Arbitrary Biot number and general reaction-rate laws,, \emph{Proc. R. Soc. Lond. A}, 390 (1983), 247. Google Scholar |
[3] |
T. Boddington, C.-G. Feng and P. Gray, Thermal explosion and the theory of its initiation by steady intense light,, \emph{Proc. R. Soc. Lond. A}, 390 (1983), 265. Google Scholar |
[4] |
T. Boddington, P. Gray and C. Robinson, Thermal explosion and the disappearance of criticality at small activation energies: exact results for the slab,, \emph{Proc. R. Soc. Lond. A}, 368 (1979), 441. Google Scholar |
[5] |
M. G. Crandall and P. H. Rabinowitz, Bifurcation, perturbation of simple eigenvalues and linearized stability,, \emph{Arch. Rational Mech. Anal.}, 52 (1973), 161.
|
[6] |
Y. Du, Exact multiplicity and S-shaped bifurcation curve for some semilinear elliptic problems from combustion theory,, \emph{SIAM J. Math. Anal.}, 32 (2000), 707.
doi: 10.1137/S0036141098343586. |
[7] |
K.-C. Hung and S.-H. Wang, A theorem on S-shaped bifurcation curve for a positone problem with convex-concave nonlinearity and its applications to the perturbed Gelfand problem,, \emph{J. Differential Equations}, 251 (2011), 223.
doi: 10.1016/j.jde.2011.03.017. |
[8] |
P. Korman and Y. Li, On the exactness of an S-shaped bifurcation curve,, \emph{Proc. Amer. Math. Soc.}, 127 (1999), 1011.
doi: 10.1090/S0002-9939-99-04928-X. |
[9] |
G. P. Miller, The structure of a stoichiometric CCI4-CH4-air flat flame,, \emph{Combust. Flame}, 101 (1995), 101. Google Scholar |
[10] |
M. Mimura and K. Sakamoto, Multi-dimensional transition layers for an exothermic reaction-diffusion system in long cylindrical domains,, \emph{J. Math. Sci. Univ. Tokyo}, 3 (1996), 109.
|
[11] |
A. L. Sánchez, A. Liñán and F. A. Williams, Chain-branching explosions in mixing layers,, \emph{SIAM J. Appl. Math.}, 59 (1999), 1335.
doi: 10.1137/S003613999732648X. |
[12] |
K. Taira, Semilinear elliptic boundary-value problems in combustion theory,, \emph{Proc. Roy. Soc. Edinburgh Sect. A}, 132 (2002), 1453.
|
[13] |
S.-H. Wang, On S-shaped bifurcation curves,, \emph{Nonlinear Anal.}, 22 (1994), 1475.
doi: 10.1016/0362-546X(94)90183-X. |
[14] |
S.-H. Wang, Rigorous analysis and estimates of S-shaped bifurcation curves in a combustion problem with general Arrhenius reaction-rate laws,, \emph{Proc. R. Soc. Lond. A}, 454 (1998), 1031. Google Scholar |
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