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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, Combust. Flame, 48 (1982), 303-304. |
[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, Proc. R. Soc. Lond. A, 390 (1983), 247-264. |
[3] |
T. Boddington, C.-G. Feng and P. Gray, Thermal explosion and the theory of its initiation by steady intense light, Proc. R. Soc. Lond. A, 390 (1983), 265-281. |
[4] |
T. Boddington, P. Gray and C. Robinson, Thermal explosion and the disappearance of criticality at small activation energies: exact results for the slab, Proc. R. Soc. Lond. A, 368 (1979), 441-461. |
[5] |
M. G. Crandall and P. H. Rabinowitz, Bifurcation, perturbation of simple eigenvalues and linearized stability, Arch. Rational Mech. Anal., 52 (1973), 161-180. |
[6] |
Y. Du, Exact multiplicity and S-shaped bifurcation curve for some semilinear elliptic problems from combustion theory, SIAM J. Math. Anal., 32 (2000), 707-733.
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, J. Differential Equations, 251 (2011), 223-237.
doi: 10.1016/j.jde.2011.03.017. |
[8] |
P. Korman and Y. Li, On the exactness of an S-shaped bifurcation curve, Proc. Amer. Math. Soc., 127 (1999), 1011-1020.
doi: 10.1090/S0002-9939-99-04928-X. |
[9] |
G. P. Miller, The structure of a stoichiometric CCI4-CH4-air flat flame, Combust. Flame, 101 (1995), 101-112. |
[10] |
M. Mimura and K. Sakamoto, Multi-dimensional transition layers for an exothermic reaction-diffusion system in long cylindrical domains, J. Math. Sci. Univ. Tokyo, 3 (1996), 109-179. |
[11] |
A. L. Sánchez, A. Liñán and F. A. Williams, Chain-branching explosions in mixing layers, SIAM J. Appl. Math., 59 (1999), 1335-1355.
doi: 10.1137/S003613999732648X. |
[12] |
K. Taira, Semilinear elliptic boundary-value problems in combustion theory, Proc. Roy. Soc. Edinburgh Sect. A, 132 (2002), 1453-1476. |
[13] |
S.-H. Wang, On S-shaped bifurcation curves, Nonlinear Anal., 22 (1994), 1475-1485.
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, Proc. R. Soc. Lond. A, 454 (1998), 1031-1048. |
show all references
References:
[1] |
T. Boddington, C.-G. Feng and P. Gray, Disappearance of criticality in thermal explosion under Frank-Kamenetskii boundary conditions, Combust. Flame, 48 (1982), 303-304. |
[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, Proc. R. Soc. Lond. A, 390 (1983), 247-264. |
[3] |
T. Boddington, C.-G. Feng and P. Gray, Thermal explosion and the theory of its initiation by steady intense light, Proc. R. Soc. Lond. A, 390 (1983), 265-281. |
[4] |
T. Boddington, P. Gray and C. Robinson, Thermal explosion and the disappearance of criticality at small activation energies: exact results for the slab, Proc. R. Soc. Lond. A, 368 (1979), 441-461. |
[5] |
M. G. Crandall and P. H. Rabinowitz, Bifurcation, perturbation of simple eigenvalues and linearized stability, Arch. Rational Mech. Anal., 52 (1973), 161-180. |
[6] |
Y. Du, Exact multiplicity and S-shaped bifurcation curve for some semilinear elliptic problems from combustion theory, SIAM J. Math. Anal., 32 (2000), 707-733.
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, J. Differential Equations, 251 (2011), 223-237.
doi: 10.1016/j.jde.2011.03.017. |
[8] |
P. Korman and Y. Li, On the exactness of an S-shaped bifurcation curve, Proc. Amer. Math. Soc., 127 (1999), 1011-1020.
doi: 10.1090/S0002-9939-99-04928-X. |
[9] |
G. P. Miller, The structure of a stoichiometric CCI4-CH4-air flat flame, Combust. Flame, 101 (1995), 101-112. |
[10] |
M. Mimura and K. Sakamoto, Multi-dimensional transition layers for an exothermic reaction-diffusion system in long cylindrical domains, J. Math. Sci. Univ. Tokyo, 3 (1996), 109-179. |
[11] |
A. L. Sánchez, A. Liñán and F. A. Williams, Chain-branching explosions in mixing layers, SIAM J. Appl. Math., 59 (1999), 1335-1355.
doi: 10.1137/S003613999732648X. |
[12] |
K. Taira, Semilinear elliptic boundary-value problems in combustion theory, Proc. Roy. Soc. Edinburgh Sect. A, 132 (2002), 1453-1476. |
[13] |
S.-H. Wang, On S-shaped bifurcation curves, Nonlinear Anal., 22 (1994), 1475-1485.
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, Proc. R. Soc. Lond. A, 454 (1998), 1031-1048. |
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