Some recent results on blow-up on the boundary for the heat equation
Banach Center Publications (2000)
- Volume: 52, Issue: 1, page 61-71
- ISSN: 0137-6934
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topChlebík, Miroslav, and Fila, Marek. "Some recent results on blow-up on the boundary for the heat equation." Banach Center Publications 52.1 (2000): 61-71. <http://eudml.org/doc/209063>.
@article{Chlebík2000,
author = {Chlebík, Miroslav, Fila, Marek},
journal = {Banach Center Publications},
keywords = {nonlinear boundary conditions; survey},
language = {eng},
number = {1},
pages = {61-71},
title = {Some recent results on blow-up on the boundary for the heat equation},
url = {http://eudml.org/doc/209063},
volume = {52},
year = {2000},
}
TY - JOUR
AU - Chlebík, Miroslav
AU - Fila, Marek
TI - Some recent results on blow-up on the boundary for the heat equation
JO - Banach Center Publications
PY - 2000
VL - 52
IS - 1
SP - 61
EP - 71
LA - eng
KW - nonlinear boundary conditions; survey
UR - http://eudml.org/doc/209063
ER -
References
top- [A] H. Amann, Parabolic evolution equations and nonlinear boundary conditions, J. Differ. Equations 72 (1988), 201-269. Zbl0658.34011
- [C] M. Chlebík, Asymptotics of blowup for the heat equation with a nonlinear boundary condition, preprint. Zbl0980.35073
- [CF1] M. Chlebík and M. Fila, From critical exponents to blow-up rates for parabolic problems, Rend. Mat. Appl., to appear. Zbl0980.35057
- [CF2] M. Chlebík and M. Fila, On the blow-up rate for the heat equation with a nonlinear boundary condition, preprint. Zbl0980.35073
- [D] K. Deng, Blow-up rates for parabolic systems, Z. angew. Math. Phys. 47 (1996), 132-143. Zbl0854.35054
- [DFL] K. Deng, M. Fila and H. A. Levine, On critical exponents for a system of heat equations coupled in the boundary conditions, Acta Math. Univ. Comenianae 63 (1994), 169-192. Zbl0824.35048
- [Fa] M. Fila, Boundedness of global solutions for the heat equation with nonlinear boundary conditions, Comment. Math. Univ. Carolinae 30 (1989), 479-484. Zbl0702.35141
- [FF] M. Fila and J. Filo, Blow-up on the boundary: A survey, in: S. Janeczko et al. (eds.), Singularities and Differential Equations, Banach Center Publ. 33, Polish Academy of Sciences, Warsaw (1996), 67-78. Zbl0858.35065
- [FFL] M. Fila, J. Filo and G. M. Lieberman, Blow-up on the boundary for the heat equation, Calc. Var. 10 (2000), 85-99. Zbl0939.35098
- [FQ1] M. Fila and P. Quittner, The blowup rate for the heat equation with a nonlinear boundary condition, Math. Methods Appl. Sci. 14 (1991), 197-205. Zbl0735.35014
- [FQ2] M. Fila and P. Quittner, Large time behavior of solutions of a semilinear parabolic equation with a nonlinear dynamical boundary condition, in: Topics in Nonlinear Analysis, The Herbert Amann Volume, Birkhäuser Verlag (1998), 252-272.
- [Fo] J. Filo, Uniform bounds for solutions of a degenerate diffusion equation with nonlinear boundary conditions, Comment. Math. Univ. Carolinae 30 (1989), 485-495. Zbl0702.35142
- [H1] B. Hu, Nonexistence of a positive solution of the Laplace equation with a nonlinear boundary condition, Diff. Int. Equations 7 (1994), 301-313. Zbl0820.35062
- [H2] B. Hu, Nondegeneracy and single-point-blowup for solution of the heat equation with a nonlinear boundary condition, J. Math. Sci. Univ. Tokyo 1 (1995), 251-276. Zbl0839.35015
- [H3] B. Hu, Remarks on the blowup estimate for solution of the heat equation with a nonlinear boundary condition, Differ. Int. Equations 9 (1996), 891-901. Zbl0852.35072
- [HY] B. Hu and H.-M. Yin, The profile near blowup time for solutions of the heat equation with a nonlinear boundary condition, Trans. Amer. Math. Soc. 346 (1994), 117-135.
- [L] H. A. Levine, Some nonexistence and instability theorems for solutions of formally parabolic equations of the form , Arch. Rat. Mech. Anal. 51 (1973), 371-386. Zbl0278.35052
- [LP1] H. A. Levine and L. E. Payne, Nonexistence theorems for the heat equation with nonlinear boundary conditions and for the porous medium equation backward in time, J. Diff. Equations 16 (1974), 319-334. Zbl0285.35035
- [LP2] H. A. Levine and L. E. Payne, Some nonexistence theorems for initial-boundary value problems with nonlinear boundary constraints, Proc. Amer. Math. Soc. 46 (1974), 277-284. Zbl0293.35004
- [LX] Z. Lin and C. Xie, The blow-up rate for a system of heat equations with nonlinear boundary conditions, Nonlin. Anal. TMA 34 (1998), 767-778. Zbl0941.35008
- [Q] P. Quittner, Global existence of solutions of parabolic problems with nonlinear boundary conditions, in: S. Janeczko et al. (eds.), Singularities and Differential Equations, Banach Center Publ. 33, Polish Academy of Sciences, Warsaw (1996), 309-314. Zbl0865.35067
- [R] J. D. Rossi, The blow-up rate for a system of heat equations with non-trivial coupling at the boundary, Math. Methods Appl. Sci. 20 (1997), 1-11. Zbl0870.35050
- [W] W. Walter, On existence and nonexistence in the large of solutions of parabolic differential equations with a nonlinear boundary condition, SIAM J. Math. Anal. 6 (1975), 85-90. Zbl0268.35052
- [WXW] S. Wang, C. Xie and M. Wang, Note on critical exponents for a system of heat equations coupled in the boundary conditions, J. Math. Anal. Appl. 218 (1998), 313-324. Zbl0891.35052
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